MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider the function f(x)=(x2+1)5/3 on the closed interval [−2,2].
Respond to each part below.
(a) Compute f′(x).
(b) Solve f′(x)=0 for x in (−2,2).
(c) Construct a sign chart for f′(x) on [−2,2] and identify every interval on which f is increasing or decreasing.
(d) Evaluate f at all critical numbers and at the endpoints. State the absolute maximum and absolute minimum values of f on [−2,2] and where they occur, justifying your answer.