Explanation Given: Function f ( x ) = x 5 − 15 x 3 Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Calculation: Function is given as f ( x ) = x 5 − 15 x 3 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( x 5 − 15 x 3 ) f ′ ( x ) = d d x ( x 5 ) − d d x ( 15 x 3 ) f ′ ( x ) = d d x ( x 5 ) − 15 d d x ( x 3 ) f ′ ( x ) = ( 5 x To determine (b) Use graph to classify the critical point for below function as a local minimum , a local maximum , or neither. f ( x ) = x 5 − 15 x 3

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.1, Problem 13P

To determine

(a)

Use the derivative to find all critical points for below function:

f(x)=x5−15x3

To determine

(b)

Use graph to classify the critical point for below function as a local minimum, a local maximum, or neither.

f(x)=x5−15x3

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Chapter 4.1, Problem 12P

Chapter 4.1, Problem 14P

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Chapter 4 Solutions

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(a) Use the derivative to find all critical points for below function: f ( x ) = x 5 − 15 x 3

Solution Summary: The author explains how the derivative is used to find all critical points for the function.

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(a)

Use the derivative to find all critical points for below function:

f(x)=x5−15x3

(b)

Use graph to classify the critical point for below function as a local minimum, a local maximum, or neither.

f(x)=x5−15x3

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Chapter 4 Solutions

(a) Use the derivative to find all critical points for below function: f ( x ) = x 5 − 15 x 3

Solution Summary: The author explains how the derivative is used to find all critical points for the function.

Concept explainers

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(a) Use the derivative to find all critical points for below function: f(x)=x5−15x3

(b) Use graph to classify the critical point for below function as a local minimum, a local maximum, or neither. f(x)=x5−15x3

Want to see the full answer?

Chapter 4 Solutions

(a)

Use the derivative to find all critical points for below function:

f(x)=x5−15x3

(b)

Use graph to classify the critical point for below function as a local minimum, a local maximum, or neither.

f(x)=x5−15x3