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.
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
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(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
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