MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider the function f(x)=x3−3x defined for all real x.
(a) Determine all intervals on which f is strictly increasing and all intervals on which it is strictly decreasing. Show analytical work that supports your conclusions.
(b) Explain why f possesses an inverse function on each interval identified in part (a).
(c) Let b=−2. Decide whether (f−1)′(b) exists. If it exists, compute its value; if it does not exist, give a clear reason.
(d) Let b=2. Decide whether (f−1)′(b) exists. If it exists, compute its value; if it does not exist, give a clear reason.