MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Examine the function f(x)=∣x3−3x∣ on the closed interval [−2,2].
(i) Determine all critical points of f inside (−2,2), including those where the derivative does not exist.
(ii) Using an appropriate test, classify each critical point obtained in part (i) as a point of local maximum, local minimum or neither.
(iii) Evaluate f at the critical points and at the endpoints to identify the absolute maximum and absolute minimum of f on [−2,2].