Question 17 of 20

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)=x²-32x² +256

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This quiz: 20 point(s) possible

This question: 1 point(s) possible

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 f is increasing on the open interval(s).

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. 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 f is decreasing on the open interval(s)

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. 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.

(Type integers or simplified fractions.)

O A. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are

OB. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f(

OC. The function has a local maximum value at one value of x. The maximum value is f() =

O D. There are no local maxima.

=

and

and fl/na. 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)=x²-32x² + 256

OD. There are no local maxima.

Find each local minimum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

(Type integers or simplified fractions.)

OA. The function has a local minimum value at one value of x. The minimum value is f(

f(

OB. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are

OC. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are

O D. There are no local minima.

at x =

at x =

If the function has extreme values, which of the extreme values, if any, are absolute? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

(Type integers or simplified fractions. Use a comma to separate answers as needed.)

and an absolute minimum of

OA. The function has an absolute maximum value of

OB. The function has an absolute maximum value of

O C. The function has no absolute maximum, but there is an absolute minimum value of

O D. There are local extreme values but there are no absolute extreme values.

O E. There are no local or absolute extreme values.

but no absolute minimum.

at x =

and

at x =

if(1)

and