Explanation Given information: Calculation: From the given graph, we can draw the first derivative graph as Since, at f ( − 1 ) the function f ( x ) is increasing, f ' ( − 1 ) > 0 f ' ( − 1 ) = 11 (approximately) Since, at f ( 0 ) the function f ( x ) is increasing, f ' ( 0 ) > 0 f ' ( 0 ) = 2 (approximately) Since, at f ( 1 ) the function f ( x ) is decreasing, f ' To determine (b) To calculate: The quantities f ' ( − 1 ) , f ' ( 0 ) , f ' ( 1 ) , f ' ( 4 ) using the formula f ( x ) = x 3 − 3 x 2 + 2 x + 10

6th Edition

ISBN: 9781119267874

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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Question

Chapter 3.1, Problem 57P

To determine

(a)

To rank:

The quantities f'(−1),f'(0),f'(1),f'(4) from smallest to largest.

To determine

(b)

To calculate:

The quantities f'(−1),f'(0),f'(1),f'(4) using the formula

f(x)=x3−3x2+2x+10

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Chapter 3.1, Problem 56P

Chapter 3.1, Problem 58P

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Chapter 3 Solutions

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(a) To rank: The quantities f ' ( − 1 ) , f ' ( 0 ) , f ' ( 1 ) , f ' ( 4 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities using the formula f(x)=x3-3+2x+10.

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(a)

To rank:

The quantities f'(−1),f'(0),f'(1),f'(4) from smallest to largest.

(b)

To calculate:

The quantities f'(−1),f'(0),f'(1),f'(4) using the formula

f(x)=x3−3x2+2x+10

Want to see the full answer?

Chapter 3 Solutions

(a) To rank: The quantities f ' ( − 1 ) , f ' ( 0 ) , f ' ( 1 ) , f ' ( 4 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities using the formula f(x)=x3-3+2x+10.

Concept explainers

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(a) To rank: The quantities f'(−1),f'(0),f'(1),f'(4) from smallest to largest.

(b) To calculate: The quantities f'(−1),f'(0),f'(1),f'(4) using the formula f(x)=x3−3x2+2x+10

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Chapter 3 Solutions

(a)

To rank:

The quantities f'(−1),f'(0),f'(1),f'(4) from smallest to largest.

(b)

To calculate:

The quantities f'(−1),f'(0),f'(1),f'(4) using the formula

f(x)=x3−3x2+2x+10