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 decreasing, f ' ( 1 ) < 0 f ' ( 1 ) = − 2 (approximately) Since, at f ( 2 ) the function f ( x ) is decreasing, f ' ( 2 ) < 0 f ' ( 2 ) = − 6 To determine (b) To calculate: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) using the formula f ( x ) = 2 e x − 3 x 2 x

6th Edition

ISBN: 9781119399322

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 3.2, Problem 36P

To determine

(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

To determine

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x

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Chapter 3.2, Problem 35P

Chapter 3.2, Problem 37P

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(a) To rank: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities f'(1),.

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(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x

Want to see the full answer?

Chapter 3 Solutions

(a) To rank: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities f'(1),.

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(a) To rank: The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b) To calculate: The quantities f'(1), f '(2) and f '(3) using the formula f(x)=2ex−3x2x

Want to see the full answer?

Chapter 3 Solutions

(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x