Explanation Given information: A graph of a derivative function is given as below, Calculation: A graph of a derivative function is given as below, From above graph it is observed that, f ' ( x ) > 0 for the interval [ − 1 , 1 ] . This means f ( x ) in increasing in whole interval. Magnitude of f ' ( x ) at any instance gives the magnitude of rate of change of f ( x ) . Means if f ' ( x ) is large in magnitude then slope will be steep and if f ' ( x ) is small then f ( x ) is gently sloping

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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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 2.2, Problem 22P

To determine

The corresponding graph of f(x) for given graph of f'(x)

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Chapter 2.2, Problem 21P

Chapter 2.2, Problem 23P

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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}. (a) (2 points) Calculate the divergence V. F. (b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that the triple integral √ (V · F) dV = √ 2²(1. = x²(1 − x² - y²) dA. E

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Chapter 2 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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The corresponding graph of f ( x ) for given graph of f ' ( x )

Solution Summary: The author explains how the graph of a derivative function f(x) is given as below.

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The corresponding graph of f(x) for given graph of f'(x)

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Chapter 2 Solutions