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.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
(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
