Explanation Given: Function f ( x ) = x 3 − 6 x + 1 Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Let us assume that p is the critical point of a continuous function f . Moving from left to right If p′ changes from negative to positive at p , then f has local minimum at p If p′ changes from positive to negative at p , then f has local maximum at p Calculation: Function is given as f ( x ) = x 3 − 6 x + 1 The graph of the above function is as follows: From the graph, we see that There are two critical point Also, function is an increasing, when x < − 2 and x > 2 And the function is decreasing when − 2 < x < 2 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( x 3 − 6 x + 1 )

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.1, Problem 15P

To determine

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x3−6x+1

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Chapter 4.1, Problem 14P

Chapter 4.1, Problem 16P

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Chapter 4 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x 3 − 6 x + 1

Solution Summary: The author explains the function's critical points and its derivative, which is undefined or zero.

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x3−6x+1

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x 3 − 6 x + 1

Solution Summary: The author explains the function's critical points and its derivative, which is undefined or zero.

Concept explainers

Videos

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f(x)=x3−6x+1

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x3−6x+1