This problem involves the function g(x) from the previous problem. Recall that g(x) is an even function on the interval [-6, 6]. The following is the graph of g(x) on [0, 6]. O 2 2 201 3 6.5 4 5.5 6 x Let h(x) be the function given by rx h(x) = _g(t) dt I (a) [1 point] Write a mathematical equation that translates the statement "g(x) is an even function." (b) [1 point] What is the domain of h(x)? (c) [1 point] What is the value of h(0)? (d) [2 points] What is h'(x)? Simplify your answer using 2a. (e) [2 points] Give a formula for h(x) involving an integal from 0 to x. (f) [2 points] Explain why h(x) is an odd function. Do not graph h(x). (g) In this part, we will study the function h(x) restricted to the interval [-3,3]. Using the graph of g(x), and the derivative h'(x) you computed in 2d, please answer the following questions: (i) [2 points] What are the critical points of h(x)? (ii) [2 points] What are the x-value(s) where h(x) attains local maximum? (iii) [2 points] What are the x-value(s) where h(x) attains local minimum? (iv) [2 points] What are the x-value(s) where h(x) attains global maximum? (v) [2 points] What are the x-value(s) where h(x) attains global minimum? (vi) [2 points] Give all intervals where h(x) is concave up?