MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider the polynomial function p(x)=x4−4x3+10. The function is defined and differentiable for all real x.
(a) Calculate all critical numbers of p.
(b) Evaluate p′′ at each critical number found in part (a).
(c) Classify each critical number as the location of a local maximum, a local minimum, or neither. Support each classification with appropriate reasoning.