Answer the following questions about the function whose derivative is f'(x)=3x(x-5). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) of f is/are x = (Simplify your answer. Use a comma to separate answers as needed.) OB. The function f has no critical points. D b. Determine where f is increasing and decreasing. Select the correct choice below and fill in the answer box to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) OA. The function f is increasing on the open interval(s) OB. The function f is decreasing on the open interval(s) OC. The function f is increasing on the open interval(s) and decreasing on the open interval(s) and never increasing. and never decreasing. c. Determine the local maximum/maxima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function f has a local maximum at x= (Simplify your answer. Use a comma to separate answers as needed.) OB. There is no local maximum. Determine the local minimum/minima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer the following questions about the function whose derivative is f'(x)=3x(x-5). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) of f is/are x = (Simplify your answer. Use a comma to separate answers as needed.) OB. The function f has no critical points. D b. Determine where f is increasing and decreasing. Select the correct choice below and fill in the answer box to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) OA. The function f is increasing on the open interval(s) OB. The function f is decreasing on the open interval(s) OC. The function f is increasing on the open interval(s) and decreasing on the open interval(s) and never increasing. and never decreasing. c. Determine the local maximum/maxima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function f has a local maximum at x= (Simplify your answer. Use a comma to separate answers as needed.) OB. There is no local maximum. Determine the local minimum/minima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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...
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Transcribed Image Text:Answer the following questions about the function whose derivative is f'(x)=3x(x-5).
a. What are the critical points of f?
b. On what open intervals is f increasing or decreasing?
c. At what points, if any, does f assume local maximum and minimum values?
a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The critical point(s) of f is/are x =
(Simplify your answer. Use a comma to separate answers as needed.)
OB. The function f has no critical points.
D
b. Determine where f is increasing and decreasing. Select the correct choice below and fill in the answer box to complete your choice.
(Type your answer in interval notation. Use a comma to separate answers as needed.)
OA. The function f is increasing on the open interval(s)
OB. The function f is decreasing on the open interval(s)
OC. The function f is increasing on the open interval(s)
and decreasing on the open interval(s)
and never increasing.
and never decreasing.
c. Determine the local maximum/maxima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The function f has a local maximum at x=
(Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no local maximum.
Determine the local minimum/minima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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