Let f(x)= 4((x-8)^(2/3))+4 (A) Find all critical values and list them below. Note: If there are no critical values, enter 'NONE'. (B) Use interval notation to indicate where f(x) is increasing. (C) Use interval notation to indicate where f(x) is decreasing. (D) List the x values of all local maxima of f. If there are no local maxima, enter 'NONE'.x values of local maximums = ? (E) List the x values of all local minima of f. If there are no local minima, enter 'NONE'.x values of local minimums = ?

Expert Answers

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A) You need to solve the equation f'(x)=0 to find teh critical values of function such that:

`f'(x) = 4*(2/3)*(x-8)^(2/3-1)`

`f'(x) = (8/3)*(x-8)^(-1/3)`

`f'(x) = 8/(3(x-8)^(1/3))`

`f'(x) = 8/(3root(3)(x-8))`

Notice that `f'(x)!=0`  for any value of x, hence the function has no critical values.

B)Notice that the function increases over R set.

C)The function does not decrease over R set.

D) Since the function has no critical values, hence the function has no maximum or minimum points.

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