The graph of the function f, consisting of three line segments and a quarter of a circle, is shown in the image. Let g be the function defined by g(x) = (integral sign (x on top/ 1 on the bottom))...

The graph of the function f, consisting of three line segments and a quarter of a circle, is shown in the image. Let g be the function defined by g(x) = (integral sign (x on top/ 1 on the bottom)) f(t) dt.

(a) Find the average rate of change of g from x = -5 to x = 5.

(b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not exist.


(c) On what open intervals, if any, is the graph of g concave up? Justify your answer.

(d) Find all x- values in the interval -5 < x="">< 5="" at="" which="" g="" has="" a="" critical="" point.="" classify="" each="" critical="" point="" as the="" location="" of="" a="" local="" minimum,="" a="" local="" maximum,="" or="" neither.="" justify="" your="">

(only solve sub part D)