Find all critical numbers of the function f(x) = x -8x. Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The critical number(s) is/are at x= There is a local maximum at x = There is no local minimum. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) There is no local maximum. There is a local minimum at x = O B. The critical number(s) is/are at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The critical number(s) is/are at x = There is a local maximum at x = There is a local minimum at (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O D. The critical number(s) is/are at x = There is no local maximum and no local minimum. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O E. There are no critical numbers.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Find all critical numbers of the function f(x) = x -8x. Then use the second-derivative test on each critical number to
determine whether it leads to a local maximum or minimum.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The critical number(s) is/are at x=
There is a local maximum at x =
There is no local minimum.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
There is no local maximum. There is a local minimum at x =
O B. The critical number(s) is/are at x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O C. The critical number(s) is/are at x =
There is a local maximum at x =
There is a local minimum at
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O D. The critical number(s) is/are at x =
There is no local maximum and no local minimum.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O E. There are no critical numbers.
Transcribed Image Text:Find all critical numbers of the function f(x) = x -8x. Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The critical number(s) is/are at x= There is a local maximum at x = There is no local minimum. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) There is no local maximum. There is a local minimum at x = O B. The critical number(s) is/are at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The critical number(s) is/are at x = There is a local maximum at x = There is a local minimum at (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O D. The critical number(s) is/are at x = There is no local maximum and no local minimum. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O E. There are no critical numbers.
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