Perform a first derivative test on the function f(x) = x/64 - x ;[-8,8]. a. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist).
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![Perform a first derivative test on the function f(x) = x/ 64 – x ;[-8,8].
a. Locate the critical points of the given function.
b. Use the first derivative test to locate the local maximum and minimum values.
c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist).
a. Locate the critical points of the given function. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
8/2 82
The critical point(s) are located at x =
2
(Use a comma to separate answers as needed.)
O B. There are no critical points.
b. Locate the local maximum and minimum values. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
A.
8/2
and local minimum(s) at x =
8/2
There are local maximum(s) at x =
2
2
(Use a comma to separate answers as needed.)
B. There are local minimum(s) at x=
There are no local maximums.
(Use a comma to separate answers as needed.)
O C. There are local maximum(s) at x =
There are no local minimums.
(Use a comma to separate answers as needed.)
D. There are no local maximums nor local minimums.
c. Identify the absolute minimum and maximum values of the function. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
A. The absolute maximum value is 32 and the absolute minimum value is - 32
(Use a comma to separate answers as needed.)
B. The absolute minimum value is
There is no absolute maximum.
(Use a comma to separate answers as needed.)
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