Explanation Given: Function f ( x ) = x 4 − 4 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 4 − 4 x 3 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( x 4 − 4 x 3 ) f ′ ( x ) = d d x ( x 4 ) − d d x ( 4 x 3 ) f ′ ( x ) = d d x ( x 4 ) − 4 d d x ( x 3 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 4 − 4 x 3

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.1, Problem 12P

To determine

(a)

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

f(x)=x4−4x3

To determine

(b)

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

f(x)=x4−4x3

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Chapter 4.1, Problem 11P

Chapter 4.1, Problem 13P

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Chapter 4 Solutions

APPLIED CALCULUS-WILEYPLUS

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(a) Use the derivative to find all critical points for below function: f ( x ) = x 4 − 4 x 3

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

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(a)

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

f(x)=x4−4x3

(b)

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

f(x)=x4−4x3

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Chapter 4 Solutions

(a) Use the derivative to find all critical points for below function: f ( x ) = x 4 − 4 x 3

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

Concept explainers

Videos

(a) Use the derivative to find all critical points for below function: f(x)=x4−4x3

(b) Use graph to classify the critical point for below function as a local minimum, a local maximum, or neither. f(x)=x4−4x3

Want to see the full answer?

Chapter 4 Solutions

(a)

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

f(x)=x4−4x3

(b)

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

f(x)=x4−4x3