Explanation Given: Function f ( x ) = ( x 2 − 4 ) 7 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 2 − 4 ) 7 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( x 2 − 4 ) 7 Using chain rule of derivative Let u = x 2 − 4 and f = u 7 f ′ ( x ) = d f d u . d u d x f ′ ( x ) = d d u ( u 7 ) . d d x ( x 2 − 4 ) f ′ ( x ) = ( 7 u 6 ) . ( 2 x − 0 ) f ′ ( x ) = 17 x u 6 f ′ ( x ) = 17 x ( x 2 − 4 ) 6 In order to find the critical points, put f ′ ( x ) = 0 Thus, we have 17 x ( x 2 − 4 ) 6 = 0 17 x = 0 or ( x 2 − 4 ) 6 = 0 x = 0 or x 2 &#

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Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 4.1, Problem 23P

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing

f(x)=(x2−4)7

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Chapter 4.1, Problem 22P

Chapter 4.1, Problem 24P

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Chapter 4 Solutions

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima . Also, check your answer by graphing f ( x ) = ( x 2 − 4 ) 7

Solution Summary: The author explains how to find all critical points for a function and then use first-derivative test to determine local maxima and minima.

Concept explainers

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing

f(x)=(x2−4)7

Want to see the full answer?

Chapter 4 Solutions

To find all critical points for below function and then use first-derivative test to determine local maxima and minima . Also, check your answer by graphing f ( x ) = ( x 2 − 4 ) 7

Solution Summary: The author explains how to find all critical points for a function and then use first-derivative test to determine local maxima and minima.

Concept explainers

Videos

To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing f(x)=(x2−4)7

Want to see the full answer?

Chapter 4 Solutions

To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing

f(x)=(x2−4)7