MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider the function f(x)=2x3−9x2+12x+1 defined for all real x.
(i) Find all critical points of f(x).
(ii) Determine the intervals on which f(x) is increasing and those on which it is decreasing.
(iii) Classify each critical point obtained in part (i) as a point of local maximum or local minimum and find the corresponding maximum or minimum value of the function.