Let f be a twice-differentiable function with f(0)=4 . The derivative of f is given by f′(x)=sin(x2−2x+1) for −2≤x≤2 . a). Find all values of x in the interval −2 0 and f′′(x)<0 . Is the approximation found in part (b) an overestimate or an underestimate for f(0.25) ? Give a reason for your answer.
(d). Using the Mean Value Theorem, explain why the average rate of change of f over the interval −2≤x≤2 cannot equal 1.25 .