Answer the question in the screenshot below. Thank you!

The graph of the function g on the interval -2 x 8 consists of a quarter circle and four line segments, as shown in the figure below. Let h be the function defined by h(x) = g(t)dtfor 2 S x S 8. (6.0) (2.-1) Graph of g a) Find the value of h'(2) or explain why it does not exist. b) At what value of x does h attain its minimum value on the interval -2 x 8? Justify your answer. c) Find the xcoordinate of all points ofinflection ofthe graph ofh for -2 < x < 8. Justify your answer. d) Let k be the function defined by k(x) = + 2. Find the value ofk'(l). Show the computations that lead to your answer. e) Find limx . Give a reason for your answer. Find the value ofh(6). g) For what value of r does the series 32r + 32r2 + + 32rn + equal the value ofh(6) found in part Show the computations that lead to your answer. h) Does the Mean Value Theorem guarantee a value of c, for -2 < c < 8, such that is equal to the average rate of change of h' over the interval -2 S x Why or why not? i) What is the value of I + (g' 2 Give a reason for your answer.