The graph of the function f, consisting of three line segments and a quarter of a...

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The graph of the function f, consisting of three line segments and a quarter of a circle, is shown above. Let g be the function defined by g(x) = S 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 answers. Graph of f The graph of the function f, consisting of three line segments and a quarter of a circle, is shown above. Let g be the function defined by g(x) = S 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 answers. Graph of f