Explanation Given: f ( x ) = 3 x 3 − x 2 + 2 x at x=1 Concept used: If f ' ( x ) > 0 ,the function is increasing. If f ' ( x ) < 0 , the function is decreasing. Calculation: f ( x ) = 3 x 3 − x 2 + 2 x f ' ( x ) = 3 ( 3 ) x 2 − ( 2 ) x + 2

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Concept explainers

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 3, Problem 8SYU

To determine

To indicate:

The given statement is true or false.

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Chapter 3, Problem 7SYU

Chapter 3, Problem 9SYU

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Chapter 3 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To indicate: The given statement is true or false.

Solution Summary: The author explains that the given statement is true or false. If f'(x)>0 is increasing, the function is decreasing.