Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Chapter 5.2, Problem 39E
To determine

To find:

The relative extrema of function f(x) with help of graph and check the answer by using analytical method for the function f(x)=x5−x4+4x3−30x2+5x+6.

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Chapter 5 Solutions

Calculus For The Life Sciences

Ch. 5.1 - YOUR TURN Find where the function is increasing...Ch. 5.1 - YOUR TURN 2 Find the intervals in which...Ch. 5.1 - Prob. 3YTCh. 5.1 - YOUR TURN Find where f is increasing and...Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Find the open intervals where the functions...Ch. 5.1 - Prob. 6E
Ch. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - For each function, find a the critical number; b...Ch. 5.1 - For each function, find a the critical number; b...Ch. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - For each function find a the critical numbers; b...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - For each function find a the critical numbers; b...Ch. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - For each function, find a the critical numbers; b...Ch. 5.1 - Prob. 33ECh. 5.1 - For each function, find a the critical numbers; b...Ch. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - A friend looks at the graph of y=x2 and observes...Ch. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Where is the function defined by f(x)=ex...Ch. 5.1 - Prob. 45ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Alcohol Concentration In Exercise 47 in Section...Ch. 5.1 - Prob. 54ECh. 5.1 - Drug Concentration Suppose a certain drug is...Ch. 5.1 - Cardiology The aortic pressure-diameter relation...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Prob. 64ECh. 5.2 - YOUR TURN Identify the x-values of all points...Ch. 5.2 - Prob. 2YTCh. 5.2 - Prob. 3YTCh. 5.2 - Prob. 4YTCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Find the x-value of all points where the function...Ch. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Find the x-value of all points where the function...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Find the x-value of all points where the function...Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Find the x-value of all points where the function...Ch. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - LIFE SCIENCE APPLICATIONS Activity Level In the...Ch. 5.2 - LIFE SCIENCE APPLICATIONS Milk Consumption The...Ch. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - LIFE SCIENCE APPLICATIONS Population Growth As we...Ch. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - OTHER APPLICATION Attitude Change Social...Ch. 5.2 - OTHER APPLICATION Height After a great deal of...Ch. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.3 - YOUR TURN Find f(1) if f(x)=5x44x3+3xCh. 5.3 - YOUR TURN Find the second derivative for a...Ch. 5.3 - YOUR TURN Find the velocity and acceleration of...Ch. 5.3 - Prob. 4YTCh. 5.3 - Prob. 5YTCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Let f(x)=lnx. a. Compute f(x), f(x), f(x),...Ch. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - In Exercise 33-56, find the open intervals where...Ch. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - In Exercise 33-56, find the open intervals where...Ch. 5.3 - Prob. 37ECh. 5.3 - In Exercise 33-56, find the open intervals where...Ch. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - In Exercise 33-56, find the open intervals where...Ch. 5.3 - In Exercises 33-56, find the open intervals where...Ch. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - In Exercises 33-56, find the open intervals where...Ch. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Find any critical numbers for f in Exercises 65-72...Ch. 5.3 - Prob. 67ECh. 5.3 - Find any critical numbers for f in Exercises 65-72...Ch. 5.3 - Find any critical numbers for f in Exercises 65-72...Ch. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Ozone Depletion According to an article in the New...Ch. 5.3 - Drug Concentration The percent of concentration of...Ch. 5.3 - Prob. 82ECh. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Breast Cancer Growth Researchers used a version of...Ch. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Phytoplankton Growth Researchers have described...Ch. 5.3 - Prob. 93ECh. 5.3 - Prob. 94ECh. 5.3 - Prob. 95ECh. 5.3 - Velocity and Acceleration When an object is...Ch. 5.3 - Prob. 97ECh. 5.3 - Prob. 98ECh. 5.3 - Prob. 99ECh. 5.3 - Prob. 100ECh. 5.3 - Point of Diminishing Returns In Exercises 100-103,...Ch. 5.3 - Prob. 102ECh. 5.3 - Point of Diminishing Returns In Exercises 100-103,...Ch. 5.4 - YOUR TURN Graph f(x)=x3+3x2+9x10.Ch. 5.4 - Prob. 2YTCh. 5.4 - YOUR TURN Graph f(x)=4x2x2+4.Ch. 5.4 - Prob. 4YTCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Graph each function, considering the domain,...Ch. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Graph each function, considering the domain,...Ch. 5.4 - Prob. 25ECh. 5.4 - Graph each function, considering the domain,...Ch. 5.4 - Prob. 27ECh. 5.4 - Graph each function, considering the domain,...Ch. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 43ECh. 5.4 - LIFE SCIENCE APPLICATIONS Neuron Communications In...Ch. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.CR - For Exercises 1-12 determine whether each of the...Ch. 5.CR - Prob. 2CRCh. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - For Exercises 1-12 determine whether each of the...Ch. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Prob. 18CRCh. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CR - Prob. 24CRCh. 5.CR - Prob. 25CRCh. 5.CR - Prob. 26CRCh. 5.CR - Prob. 27CRCh. 5.CR - Prob. 28CRCh. 5.CR - Prob. 29CRCh. 5.CR - Prob. 30CRCh. 5.CR - Prob. 31CRCh. 5.CR - Prob. 32CRCh. 5.CR - Prob. 33CRCh. 5.CR - Prob. 34CRCh. 5.CR - Prob. 35CRCh. 5.CR - Prob. 36CRCh. 5.CR - Prob. 37CRCh. 5.CR - Prob. 38CRCh. 5.CR - Prob. 39CRCh. 5.CR - Prob. 40CRCh. 5.CR - Prob. 41CRCh. 5.CR - Prob. 42CRCh. 5.CR - Prob. 43CRCh. 5.CR - Prob. 44CRCh. 5.CR - Prob. 45CRCh. 5.CR - Prob. 48CRCh. 5.CR - Graph each function, considering the domain,...Ch. 5.CR - Prob. 50CRCh. 5.CR - Prob. 71CRCh. 5.CR - Prob. 73CRCh. 5.CR - Prob. 74CRCh. 5.CR - Prob. 75CRCh. 5.CR - Prob. 76CRCh. 5.CR - Prob. 77CRCh. 5.CR - Prob. 78CRCh. 5.CR - Prob. 79CRCh. 5.CR - Prob. 80CRCh. 5.CR - Prob. 81CRCh. 5.CR - Prob. 82CRCh. 5.EA - Prob. 1EACh. 5.EA - Prob. 2EACh. 5.EA - Prob. 3EA
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY