A table: x -3 0 3 6

f(x) -5 4 1 7

f'(x) -1 2 -2 4

The table above gives value of a twice-differentiable function f and its first derivative f' for selected values of x. Let g be the function defined by g(x) = f(x^2 - x)

(a) What is the value of g'(3)?

(b) It is known that g'' (0) = -1. What is the value of f''(0)?

(c) Is there a value of c, for 0

(d) Let h be the function with derivative given by h'(x) = 4e^cosx. At what value of x in the interval -3<_ x<_0 does the instantaneous rate of change of h equal the average rate of change of f over the interval -3<_x<_0?