MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider the function
f(x)=x3−3x2+2.
(i) Find all the critical points of f(x).
(ii) Evaluate f′′(x) and hence find f′′ at each critical point obtained in part (i).
(iii) At every critical point where f′′=0, use a suitable method to decide whether the point is a local maximum, a local minimum or neither. Give complete justification of your answer.
(iv) Determine the corresponding local maximum or minimum value of the function, if any.