Essential Calculus
Essential Calculus
2nd Edition
ISBN: 9781133490975
Author: Stewart, James
Publisher: Cengage Learning
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Concept explainers

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 11, Problem 6RE

Sketch several level curves of the function.

6. f(x, y) = ex + y

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Chapter 11 Solutions

Essential Calculus

Ch. 11.1 - Let g(x, y) = cos(x + 2y). (a) Evaluate g(2, 1)....Ch. 11.1 - Let F(x,y)=1+4y2. (a) Evaluate F(3,1). (b) Find...Ch. 11.1 - Let f(x,y,z)=x+y+z+ln(4x2y2z2). (a) Evaluate f(1,...Ch. 11.1 - Let g(x,y,z)=x3y2z10xyz. (a) Evaluate g(1, 2, 3)....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 15....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 19....Ch. 11.1 - Find and sketch the domain of the function. f(x,...
Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 22....Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 15ECh. 11.1 - Sketch the graph of the function. f(x, y) = eyCh. 11.1 - 1320 Sketch the graph of the function. 17. f(x, y)...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 19ECh. 11.1 - A contour map for a function f is shown. Use it to...Ch. 11.1 - Two contour maps are shown. One is for a function...Ch. 11.1 - Locate the points A and B on the map of Lonesome...Ch. 11.1 - Make a rough sketch of a contour map for the...Ch. 11.1 - Prob. 25ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Prob. 28ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Prob. 30ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Sketch both a contour map and a graph of the...Ch. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Use a computer to graph the function using various...Ch. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 56ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Find the first partial derivatives of the...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Find the indicated partial derivative. 32. f(x, y)...Ch. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - 3738 Find fx and fy and graph f, fx, and fy with...Ch. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Use implicit differentiation to find z/x and z/y....Ch. 11.3 - Use implicit differentiation to find z/x and z/y....Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Find z/x and z/y. 52. (a) z = f(x)g(y) (b) z =...Ch. 11.3 - Prob. 45ECh. 11.3 - Find all the second partial derivatives. 54. f(x,...Ch. 11.3 - Find all the second partial derivatives. 55....Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Verify that the conclusion of Clairauts Theorem...Ch. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Prob. 56ECh. 11.3 - Prob. 57ECh. 11.3 - Find the indicated partial derivative(s). 70. u =...Ch. 11.3 - Prob. 59ECh. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Determine whether each of the following functions...Ch. 11.3 - Verify that the function u=1/x2+y2+z2 is a...Ch. 11.3 - Prob. 64ECh. 11.3 - Prob. 65ECh. 11.3 - Prob. 66ECh. 11.3 - Show that the function z = xey + yex is a solution...Ch. 11.3 - Prob. 68ECh. 11.3 - Prob. 69ECh. 11.3 - Prob. 71ECh. 11.3 - Prob. 70ECh. 11.3 - The wind-chill index is modeled by the function W...Ch. 11.3 - Prob. 73ECh. 11.3 - Prob. 74ECh. 11.3 - Prob. 75ECh. 11.3 - Prob. 76ECh. 11.3 - Prob. 77ECh. 11.3 - Prob. 78ECh. 11.3 - Prob. 79ECh. 11.3 - Prob. 80ECh. 11.3 - Prob. 81ECh. 11.3 - Prob. 82ECh. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Prob. 3ECh. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 11ECh. 11.4 - Explain why the function is differentiable at the...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 15ECh. 11.4 - Verify the linear approximation at (0, 0). 16....Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Find the differential of the function. 26....Ch. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - If z = x2 xy + 3y2 and (x, y) changes from (3, 1)...Ch. 11.4 - The length and width of a rectangle are measured...Ch. 11.4 - Use differentials to estimate the amount of metal...Ch. 11.4 - Prob. 29ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 31ECh. 11.4 - Suppose you need to know an equation of the...Ch. 11.4 - Show that the function is differentiable by...Ch. 11.4 - Show that the function is differentiable by...Ch. 11.4 - Prob. 37ECh. 11.4 - (a) The function...Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 1....Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 2....Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 5. w =...Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 6. w =...Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 5....Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 6....Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 11. z = er...Ch. 11.5 - Prob. 8ECh. 11.5 - If z = f(x, y), where f is differentiable, and...Ch. 11.5 - Let W(s,t)=F(u(s,t),(s,t)), where F, u and are...Ch. 11.5 - Suppose f is a differentiable function of x and y,...Ch. 11.5 - Suppose f is a differentiable function of x and y,...Ch. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use Equation 6 to find dy/dx. 28. cos(xy) = 1 +...Ch. 11.5 - Use Equation 6 to find dy/dx. 29. tan1(x2y) = x +...Ch. 11.5 - Use Equation 6 to find dy/dx. 30. ey sin x = x +...Ch. 11.5 - Use Equations 7 to find z/x and z/y. 31. x2 + 2y2...Ch. 11.5 - Use Equations 7 to find z/y and z/y. 26....Ch. 11.5 - Use Equations 7 to find z/x and z/y. 33. ez = xyzCh. 11.5 - Use Equations 7 to find z/x and z/y. 34. yz + x ln...Ch. 11.5 - The temperature at a point (x, y) is T(x, y),...Ch. 11.5 - Prob. 30ECh. 11.5 - The speed of sound traveling through ocean water...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - The voltage V in a simple electrical circuit is...Ch. 11.5 - The pressure of 1 mole of an ideal gas is...Ch. 11.5 - A sound with frequency fs, is produced by a source...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Prob. 40ECh. 11.5 - Prob. 41ECh. 11.5 - Prob. 42ECh. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11.5 - Prob. 45ECh. 11.5 - Prob. 46ECh. 11.5 - Prob. 47ECh. 11.5 - Prob. 48ECh. 11.6 - Find the directional derivative of f at the given...Ch. 11.6 - Find the directional derivative of f at the given...Ch. 11.6 - (a) Find the gradient of f. (b) Evaluate the...Ch. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - (a) Find the gradient of f. (b) Evaluate the...Ch. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Find the directional derivative of the function at...Ch. 11.6 - Use the figure to estimate Du, f(2, 2).Ch. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 15ECh. 11.6 - Find the maximum rate of change of f at the given...Ch. 11.6 - Find the maximum rate of change of f at the given...Ch. 11.6 - (a) Show that a differentiable function f...Ch. 11.6 - Find the directions in which the directional...Ch. 11.6 - Find all points at which the direction of fastest...Ch. 11.6 - Near a buoy, the depth of a lake at the point with...Ch. 11.6 - The temperature T in a metal ball is inversely...Ch. 11.6 - Prob. 24ECh. 11.6 - Suppose that over a certain region of space the...Ch. 11.6 - Suppose you are climbing a hill whose shape is...Ch. 11.6 - Prob. 27ECh. 11.6 - Shown is a topographic map of Blue River Pine...Ch. 11.6 - Show that the operation of taking the gradient of...Ch. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Use a computer to graph the surface, the tangent...Ch. 11.6 - Use a computer to graph the surface, the tangent...Ch. 11.6 - If f(x, y) = xy, find the gradient vector f(3, 2)...Ch. 11.6 - If g(x, y) = x2 + y2 4x, find the gradient vector...Ch. 11.6 - Show that the equation of the tangent plane to the...Ch. 11.6 - At what point on the paraboloid y=x2+z2 is the...Ch. 11.6 - Are there any points on the hyperboloid x2 y2 z2...Ch. 11.6 - Show that the ellipsoid 3x2 + 2y2 + z2 = 9 and the...Ch. 11.6 - Where does the normal line to the paraboloid z =...Ch. 11.6 - Prob. 46ECh. 11.6 - Show that the sum of the x-, y-, and z-intercepts...Ch. 11.6 - Prob. 48ECh. 11.6 - Find parametric equations tor the tangent line to...Ch. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11.6 - Suppose that the directional derivatives of f(x,...Ch. 11.6 - Prob. 54ECh. 11.7 - Suppose (1, 1) is a critical point of a function f...Ch. 11.7 - Use the level curves in the figure to predict the...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Prob. 9ECh. 11.7 - Prob. 10ECh. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Prob. 13ECh. 11.7 - Prob. 14ECh. 11.7 - Prob. 15ECh. 11.7 - Prob. 16ECh. 11.7 - Prob. 17ECh. 11.7 - Use a graph or level curves or both to estimate...Ch. 11.7 - Prob. 19ECh. 11.7 - Prob. 20ECh. 11.7 - Use a graphing device as in Example 4 (or Newtons...Ch. 11.7 - Use a graphing device as in Example 4 (or Newtons...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Prob. 29ECh. 11.7 - Prob. 30ECh. 11.7 - Prob. 31ECh. 11.7 - Prob. 32ECh. 11.7 - Prob. 33ECh. 11.7 - Prob. 34ECh. 11.7 - Prob. 35ECh. 11.7 - Prob. 36ECh. 11.7 - Prob. 37ECh. 11.7 - Prob. 38ECh. 11.7 - Prob. 39ECh. 11.7 - Prob. 40ECh. 11.7 - Prob. 41ECh. 11.7 - The base of an aquarium with given volume V is...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Prob. 46ECh. 11.7 - Prob. 47ECh. 11.7 - Prob. 48ECh. 11.8 - Pictured are a contour map of f and a curve with...Ch. 11.8 - Prob. 21ECh. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Each of these extreme value problems has a...Ch. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Prob. 4ECh. 11.8 - Each of these extreme value problems has a...Ch. 11.8 - Prob. 6ECh. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Prob. 8ECh. 11.8 - Prob. 9ECh. 11.8 - Prob. 10ECh. 11.8 - Prob. 11ECh. 11.8 - Prob. 12ECh. 11.8 - Find the extreme values of f subject to both...Ch. 11.8 - Prob. 14ECh. 11.8 - Prob. 15ECh. 11.8 - Prob. 16ECh. 11.8 - Find the extreme values of f on the region...Ch. 11.8 - Prob. 18ECh. 11.8 - Prob. 19ECh. 11.8 - Prob. 22ECh. 11.8 - Prob. 23ECh. 11.8 - Prob. 25ECh. 11.8 - Prob. 26ECh. 11.8 - Use Lagrange multipliers to prove that the...Ch. 11.8 - Use Lagrange multipliers to prove that the...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Prob. 37ECh. 11.8 - Prob. 38ECh. 11.8 - Prob. 39ECh. 11.8 - Prob. 40ECh. 11.8 - Prob. 41ECh. 11.8 - Prob. 42ECh. 11.8 - The plane x + y + 2z = 2 intersects the paraboloid...Ch. 11.8 - Prob. 44ECh. 11.8 - (a) Find the maximum value of...Ch. 11.8 - Prob. 48ECh. 11 - Prob. 1RCCCh. 11 - What is a function of three variables? How can you...Ch. 11 - Prob. 3RCCCh. 11 - (a) What does it mean to say that f is continuous...Ch. 11 - Prob. 5RCCCh. 11 - What does Clairauts Theorem say?Ch. 11 - Prob. 7RCCCh. 11 - Define the linearization of f at (a, b). What is...Ch. 11 - Prob. 9RCCCh. 11 - If z = f(x, y), what arc the differentials dx, dy,...Ch. 11 - State the Chain Rule for the case where z = f(x,...Ch. 11 - If z is defined implicitly as a function of x and...Ch. 11 - Prob. 13RCCCh. 11 - Prob. 14RCCCh. 11 - Prob. 15RCCCh. 11 - Prob. 16RCCCh. 11 - State the Second Derivatives Test.Ch. 11 - (a) What is a closed set in 2? What is a bounded...Ch. 11 - Explain how the method of Lagrange multipliers...Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 2RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 8RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Find and sketch the domain of the function. 1....Ch. 11 - Find and sketch the domain of the function. 2....Ch. 11 - Sketch the graph of the function. 3. f(x, y) = 1 ...Ch. 11 - Sketch the graph of the function. 4. f(x, y) = x2...Ch. 11 - Sketch several level curves of the function. 5....Ch. 11 - Sketch several level curves of the function. 6....Ch. 11 - Make a rough sketch of a contour map for the...Ch. 11 - The contour map of a function f is shown, (a)...Ch. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - The speed of sound traveling through ocean water...Ch. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - If z = xy + xey/x show that xzx+yzy=xy+z.Ch. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Find du if u = ln(1 + se2t).Ch. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - If v = x2sin y + yexy, where x = s + 2t and y =...Ch. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - The length x of a side of a triangle is increasing...Ch. 11 - Prob. 39RECh. 11 - If cos(xyz) = 1 + .x2y2 + z2, find zx and zy.Ch. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Find the directional derivative of f at the given...Ch. 11 - Find the maximum rate of change of f(x,y)=x2y+y at...Ch. 11 - Find parametric equations of the tangent line at...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the absolute maximum and minimum values of f...Ch. 11 - Find the absolute maximum and minimum values of f...Ch. 11 - Use a graph or level curves or both to estimate...Ch. 11 - Use a graphing calculator or computer (or Newtons...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Prob. 59RECh. 11 - A package in the shape of a rectangular box can be...Ch. 11 - A pentagon is formed by placing an isosceles...Ch. 11 - Prob. 62RE
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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY