Calculus (MindTap Course List)
Calculus (MindTap Course List)
11th Edition
ISBN: 9781337275347
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 2.1, Problem 92E

Conjecture Consider the functions f ( x ) = x 2 and g ( x ) = x 3 .

(a) Graph f and f' on the same set of axes.

(b) Graph g and g' on the same set of axes.

(c) Identify a pattern between f and g and their respective derivatives. Use the pattern to make a conjecture about h' (x) if h ( x ) = x n . where " is an integer and n ≥ 2 ?

(d) Find f'(x) if f ( x ) = x 4 Compare the result will) the conjecture in part (c). Is this a proof of your conjecture? Explain.

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Chapter 2 Solutions

Calculus (MindTap Course List)

Ch. 2.1 - Tangent Line Describe how to find the slope of the...Ch. 2.1 - Notation List four notation alternatives to f(x).Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Estimating Slope In Exercises 5 and 6, estimate...Ch. 2.1 - Estimating Slope In Exercises 5 and 6, estimate...Ch. 2.1 - Slopes of Secant Lines In Exercises 7 and 8, use...Ch. 2.1 - Slopes of Secant Lines In Exercises 7 and 8. use...Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...
Ch. 2.1 - Prob. 11ECh. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 17ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 20ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 30ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 37ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Sketching a Derivative In Exercises 43-48, sketch...Ch. 2.1 - Prob. 48ECh. 2.1 - Sketching a Graph Sketch a graph of a function...Ch. 2.1 - Sketching a Graph Sketch a graph of a function...Ch. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - Using a Tangent Line The tangent line to the graph...Ch. 2.1 - Working Backwards In Exercises 55-58, the Unlit...Ch. 2.1 - Prob. 56ECh. 2.1 - Prob. 57ECh. 2.1 - Working Backwards In Exercises 55-58, the Unlit...Ch. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 63ECh. 2.1 - HOW DO YOU SEE IT? The figure shows die graph of...Ch. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - Using the Alternative Form of the Derivative In...Ch. 2.1 - Prob. 70ECh. 2.1 - Prob. 71ECh. 2.1 - Prob. 72ECh. 2.1 - Prob. 73ECh. 2.1 - Prob. 74ECh. 2.1 - Prob. 75ECh. 2.1 - Using the Alternative Form of the Derivative In...Ch. 2.1 - Determining Differentiability In Exercises 77-80,...Ch. 2.1 - Determining Differentiability In Exercises 77-80,...Ch. 2.1 - Prob. 79ECh. 2.1 - Determining Differentiability In Exercises 77-80,...Ch. 2.1 - Prob. 81ECh. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.1 - Prob. 85ECh. 2.1 - Determining Differentiability In Exercises 85-88,...Ch. 2.1 - Prob. 87ECh. 2.1 - Prob. 88ECh. 2.1 - Prob. 89ECh. 2.1 - Determining Differentiability In Exercises 89 and...Ch. 2.1 - Prob. 91ECh. 2.1 - Conjecture Consider the functions f(x)=x2 and...Ch. 2.1 - True or False? In Exercises 93-96, determine...Ch. 2.1 - Prob. 94ECh. 2.1 - Prob. 95ECh. 2.1 - True or False? In Exercises 93-96. determine...Ch. 2.1 - Differentiability and Continuity Let...Ch. 2.1 - Prob. 98ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Estimating Slope In Exercises 5 and 6, use the...Ch. 2.2 - Estimating Slope In Exercises 5 and 6, use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Prob. 13ECh. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Prob. 17ECh. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Finding a Derivative In Exercises 39-54, find the...Ch. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.2 - Horizontal Tangent Line In Exercises 59-64....Ch. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Horizontal Tangent Line In Exercises 59-64....Ch. 2.2 - Prob. 65ECh. 2.2 - Finding a Value In Exercises 65-68, find k such...Ch. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Sketching a Graph Sketch the graph of a function f...Ch. 2.2 - HOW DO YOU SEE IT? Use the graph of f to answer...Ch. 2.2 - Prob. 77ECh. 2.2 - Prob. 78ECh. 2.2 - Horizontal Tangent Line Show that the graph of the...Ch. 2.2 - Prob. 80ECh. 2.2 - Prob. 81ECh. 2.2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.2 - Linear Approximation Consider the function...Ch. 2.2 - Linear Approximation Repeat Exercise 83 for the...Ch. 2.2 - True or False? In Exercises 85-90, determine...Ch. 2.2 - Prob. 86ECh. 2.2 - Prob. 87ECh. 2.2 - Prob. 88ECh. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Finding Rates of Change In Exercises 91-94, find...Ch. 2.2 - Finding Rates of Change In Exercises 91-94, find...Ch. 2.2 - Prob. 93ECh. 2.2 - Prob. 94ECh. 2.2 - Vertical Motion In Exercises 95 and 96, use the...Ch. 2.2 - Vertical Motion In Exercises 95 and 96, use the...Ch. 2.2 - Vertical Motion In Exercises 97 and 98, use the...Ch. 2.2 - Vertical Motion In Exercises 97 and 98, use the...Ch. 2.2 - Think About It The graph of the position function...Ch. 2.2 - Prob. 100ECh. 2.2 - Prob. 101ECh. 2.2 - Area The area of a square with sides of length s...Ch. 2.2 - Modeling Data The stopping distance of an...Ch. 2.2 - Prob. 104ECh. 2.2 - Prob. 105ECh. 2.2 - Prob. 106ECh. 2.2 - Prob. 107ECh. 2.2 - Prob. 108ECh. 2.2 - Prob. 109ECh. 2.2 - Prob. 110ECh. 2.2 - Making a Function Differentiable In Exercises 111...Ch. 2.2 - Prob. 112ECh. 2.2 - Prob. 113ECh. 2.2 - Prob. 114ECh. 2.2 - Prob. 115ECh. 2.3 - CONCEPT CHECK Product Rule Describe the Product...Ch. 2.3 - Prob. 2ECh. 2.3 - CONCEPT CHECK Trigonometric Functions What are the...Ch. 2.3 - CONCEPT CHECK Higher-Order Derivative What is a...Ch. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Using the Quotient Rule In Exercises 11-16, use...Ch. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Finding and Evaluating a Derivative In Exercises...Ch. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Finding a Derivative In Exercises 29-40, Find the...Ch. 2.3 - Prob. 30ECh. 2.3 - Finding a Derivative In Exercises 29-40, Find the...Ch. 2.3 - Prob. 32ECh. 2.3 - Finding a Derivative In Exercises 29-40, Find the...Ch. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Finding a Derivative In Exercises 29-40, Find the...Ch. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Finding a Derivative of a Trigonometric Function...Ch. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Finding a Derivative of a Trigonometric Function...Ch. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Finding the Slope of a Graph In Exercises 59-62,...Ch. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Prob. 65ECh. 2.3 - Prob. 66ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Prob. 70ECh. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 73ECh. 2.3 - Prob. 74ECh. 2.3 - Prob. 75ECh. 2.3 - Prob. 76ECh. 2.3 - Prob. 77ECh. 2.3 - Prob. 78ECh. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - Finding Derivatives In Exercises 81 and 82, use...Ch. 2.3 - Prob. 82ECh. 2.3 - Prob. 83ECh. 2.3 - Prob. 84ECh. 2.3 - Inventory Replenishment The ordering and...Ch. 2.3 - Prob. 86ECh. 2.3 - Prob. 87ECh. 2.3 - Rate of Change Determine whether there exist any...Ch. 2.3 - Prob. 89ECh. 2.3 - Satellites When satellites observe Earth, they can...Ch. 2.3 - Prob. 91ECh. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Prob. 93ECh. 2.3 - Prob. 94ECh. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Prob. 96ECh. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Prob. 98ECh. 2.3 - Prob. 99ECh. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Prob. 101ECh. 2.3 - Prob. 102ECh. 2.3 - Prob. 103ECh. 2.3 - Prob. 104ECh. 2.3 - Prob. 105ECh. 2.3 - Prob. 106ECh. 2.3 - Using Relationships In Exercises 105-108, use the...Ch. 2.3 - Prob. 108ECh. 2.3 - Prob. 109ECh. 2.3 - Differentiation of Piecewise Functions Describe...Ch. 2.3 - Prob. 111ECh. 2.3 - Identifying Graphs In Exercises 111 and 112, the...Ch. 2.3 - Prob. 113ECh. 2.3 - Prob. 114ECh. 2.3 - Prob. 115ECh. 2.3 - Sketching a Graph Sketch the graph of a...Ch. 2.3 - Prob. 117ECh. 2.3 - Prob. 118ECh. 2.3 - Prob. 119ECh. 2.3 - HOW DO YOU SEE IT? The figure shows the graphs of...Ch. 2.3 - Prob. 121ECh. 2.3 - Finding a Pattern In Exercises 121 and 122....Ch. 2.3 - Prob. 123ECh. 2.3 - Finding a Pattern Develop a general rule for the...Ch. 2.3 - Prob. 125ECh. 2.3 - Prob. 126ECh. 2.3 - Prob. 127ECh. 2.3 - Prob. 128ECh. 2.3 - Prob. 129ECh. 2.3 - Prob. 130ECh. 2.3 - Prob. 131ECh. 2.3 - Prob. 132ECh. 2.3 - Prob. 133ECh. 2.3 - Prob. 134ECh. 2.3 - Prob. 135ECh. 2.3 - Prob. 136ECh. 2.3 - Prob. 137ECh. 2.3 - Prob. 138ECh. 2.4 - Chain Rule Describe the Chain Rule for the...Ch. 2.4 - General Power Rule What is the difference between...Ch. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Finding a Derivative In Exercises 9-34, find the...Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 48ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 55ECh. 2.4 - Finding a Derivative Using Technology In Exercises...Ch. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.4 - Prob. 59ECh. 2.4 - Prob. 60ECh. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Prob. 63ECh. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Prob. 78ECh. 2.4 - Prob. 79ECh. 2.4 - Prob. 80ECh. 2.4 - Prob. 81ECh. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Finding a Second Derivative In Exercises 83-88,...Ch. 2.4 - Prob. 88ECh. 2.4 - Prob. 89ECh. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.4 - Prob. 92ECh. 2.4 - Prob. 93ECh. 2.4 - Identifying Graphs In Exercises 93 and 94, the...Ch. 2.4 - Describing a Relationship In Exercises 99 and 100,...Ch. 2.4 - Prob. 96ECh. 2.4 - Think about It The table shows some values of the...Ch. 2.4 - Prob. 98ECh. 2.4 - Finding Derivatives In Exercises 99 and 100, the...Ch. 2.4 - Prob. 100ECh. 2.4 - Doppler Effect The frequency F of a fire truck...Ch. 2.4 - Prob. 102ECh. 2.4 - Prob. 103ECh. 2.4 - Wave Motion A buoy oscillates in simple harmonic...Ch. 2.4 - Prob. 105ECh. 2.4 - Prob. 106ECh. 2.4 - Prob. 107ECh. 2.4 - Prob. 108ECh. 2.4 - Prob. 109ECh. 2.4 - Conjecture Let f be a differentiable function of...Ch. 2.4 - Prob. 111ECh. 2.4 - Prob. 112ECh. 2.4 - Even and Odd Functions (a) Show that the...Ch. 2.4 - Prob. 114ECh. 2.4 - Prob. 115ECh. 2.4 - Prob. 116ECh. 2.4 - Prob. 117ECh. 2.4 - Prob. 118ECh. 2.4 - Prob. 119ECh. 2.4 - Prob. 120ECh. 2.4 - True or False? In Exercises 121-124. determine...Ch. 2.4 - Prob. 122ECh. 2.4 - Prob. 123ECh. 2.4 - Prob. 124ECh. 2.4 - Prob. 125ECh. 2.4 - Prob. 126ECh. 2.5 - CONCEPT CHECK Explicit and Implicit Functions...Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 6ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 8ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 10ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 16ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 18ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 20ECh. 2.5 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Finding the Slope of a Graph In Exercises 25-32,...Ch. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Finding the Slope of a Graph In Exercises 25-32,...Ch. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Famous Curves In Exercises 39-42, find the slope...Ch. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Ellipse (a) Use implicit differentiation to find...Ch. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Finding a Second Derivative In Exercises 49-54....Ch. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Finding a Second Derivative In Exercises 49-54,...Ch. 2.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Prob. 56ECh. 2.5 - Tangent Lines and Normal Lines In Exercises 63 and...Ch. 2.5 - Tangent Lines and Normal Lines In Exercises 57 and...Ch. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Orthogonal Trajectories The figure below shows the...Ch. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 72ECh. 2.5 - Prob. 73ECh. 2.5 - Prob. 74ECh. 2.5 - Prob. 75ECh. 2.5 - Normals to a Parabola The graph shows die normal...Ch. 2.5 - Prob. 77ECh. 2.6 - Related-Rate Equation What is a related-rate...Ch. 2.6 - Related Rates In your own words, state the...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Prob. 5ECh. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Moving Point In Exercises 710, a point is moving...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Area The radius r of a circle is increasing at a...Ch. 2.6 - Area The length .v of each side of an equilateral...Ch. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Height At a sand and gravel plant, sand is falling...Ch. 2.6 - Height The volume of oil in a cylindrical...Ch. 2.6 - Depth A swimming pool is 12 meters long, 6 meters...Ch. 2.6 - Depth A trough is 12 feet long and 3 feet across...Ch. 2.6 - Moving Ladder A ladder 25 feet long is leaning...Ch. 2.6 - Construction A construction worker pulls a...Ch. 2.6 - Construction A winch at the top of a 12-meter...Ch. 2.6 - Boating A boat is pulled into a dock by means of a...Ch. 2.6 - Air Traffic Control An air traffic controller...Ch. 2.6 - Air Traffic Control An airplane is flying at an...Ch. 2.6 - Sports A baseball diamond has the shape of a...Ch. 2.6 - Prob. 28ECh. 2.6 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.6 - Shadow Length Repeal Exercise 29 for a man 6 feet...Ch. 2.6 - Machine Design The endpoints of a movable rod of...Ch. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - HOW DO YOU SEE IT? Using the graph of f, (a)...Ch. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Flight Control An airplane is flying in still air...Ch. 2.6 - Prob. 40ECh. 2.6 - Angle of Elevation A fish is reeled in at a rate...Ch. 2.6 - Angle of Elevation An airplane flies at an...Ch. 2.6 - Linear vs. Angular Speed A patrol car is parked 50...Ch. 2.6 - Linear vs. Angular Speed A wheel of radius 30...Ch. 2.6 - Prob. 45ECh. 2.6 - Security Camera A security camera is centered 50...Ch. 2.6 - Prob. 47ECh. 2.6 - Moving Shadow A ball is dropped from a height of...Ch. 2.6 - Acceleration In Exercises 49 and 50, find the...Ch. 2.6 - Acceleration In Exercises 49 and 50, find the...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Determining Differentiability In Exercises 7 and...Ch. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Vibrating String When a guitar string is plucked,...Ch. 2 - Prob. 26RECh. 2 - Vertical Motion In Exercises 27 and 28, use the...Ch. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Finding a Second Derivative In Exercises 4552,...Ch. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Harmonic Motion The displacement from equilibrium...Ch. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Prob. 88RECh. 2 - Prob. 89RECh. 2 - Prob. 90RECh. 2 - Prob. 1PSCh. 2 - Finding Equations of Tangent Lines Graph the two...Ch. 2 - Finding a Polynomial Find a third-degree...Ch. 2 - Prob. 4PSCh. 2 - Tangent Lines and Normal Lines (a) Find an...Ch. 2 - Finding Polynomials (a) Find the polynomial...Ch. 2 - Prob. 7PSCh. 2 - Prob. 8PSCh. 2 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2 - Moving Point A particle is moving along the graph...Ch. 2 - Prob. 11PSCh. 2 - Proof Let E be a function satisfying E(0)=E(0)=1....Ch. 2 - Prob. 13PSCh. 2 - Prob. 14PSCh. 2 - Acceleration and Jerk If a is the acceleration of...
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