# 12.a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.g(x) x18-x2a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The function g is increasing on the open interval(s)(Type your answer in interval notation. Type an exact answer in simplified form. Use a comma to separate answers as needed.)B. 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 to complete your choice.O A. The function g is decreasing on the open interval(s)(Type your answer in interval notation. Type an exact answer in simplified form. Use a comma to separate answers as needed.)O B. The function is never decreasing.b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are gand(Type exact answers in simplified form.)B. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are gandg(Type exact answers in simplified form.)C. The function has a local maximum value at one value of x. The maximum value is g=(Type exact answers in simplified form.)D. There are no local maxima.Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The function has a local minimum value at one value of x. The minimum value is(Type exact answers in simplified form.)B. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are g(Type exact answers in simplified form.)and gC. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are gand(Type exact answers in simplified form.)D. There are no local minima.

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Asked Oct 28, 2019
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## Expert Answer

Step 1

Given function is

Step 2

For increasing and decreasing of function, derivate the above function

Step 3

Critical points are the points where function is define...

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