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a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x¹/3 (x²-9) a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function is increasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never decreasing. b. Find each local maximum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Simplify your answers. Type exact answers, using radicals as needed.) OA. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f(0) = [ O B. The function has a local maximum value at one value of x. The maximum value is f() = OC. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f() = f(1) =, and f(1) O D. There are no local maxima. and

a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x¹/3 (x²-9) a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function is increasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never decreasing. b. Find each local maximum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Simplify your answers. Type exact answers, using radicals as needed.) OA. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f(0) = [ O B. The function has a local maximum value at one value of x. The maximum value is f() = OC. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f() = f(1) =, and f(1) O D. There are no local maxima. and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x¹/3 (x²-9) a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is increasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never decreasing. b. Find each local maximum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Simplify your answers. Type exact answers, using radicals as needed.) O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f B. The function has a local maximum value at one value of x. The maximum value is f(): C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are D. There are no local maxima. = and e f(1) = f(1) = , and f(1) = 1.
Transcribed Image Text:a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x¹/3 (x²-9) a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is increasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never decreasing. b. Find each local maximum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Simplify your answers. Type exact answers, using radicals as needed.) O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f B. The function has a local maximum value at one value of x. The maximum value is f(): C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are D. There are no local maxima. = and e f(1) = f(1) = , and f(1) = 1.
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