(x) -3 0 3 6 f(x) -5 4 1 7
f'(x) -1 2 -2 4
The table above gives values 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 c , for 0 (d) Let h be the function with derivative given by h′(x)=4ecosx . 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 ?