MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let f(x)=x3−6x2+9x+2 be defined on the closed interval [−1,5]. Answer the following questions to determine the absolute extrema of f on this interval.
(a) Calculate f′(x) and determine all critical numbers that lie in the open interval (−1,5).
(b) Evaluate f at each endpoint and at every critical number found in part (a).
(c) State the coordinates of the absolute maximum and absolute minimum points of f on [−1,5], and justify your classification using the values obtained in part (b).