MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=x4+x2, −2≤x≤2.
(1) Part 1: (a) Compute f′(x) and find every critical point of f in the open interval (−2,2).
(2) Part 2: (b) Use the second derivative to classify each critical point found in part (a).
(3) Part 3: (c) Determine the absolute maximum and absolute minimum values of f on [−2,2], stating where each occurs and providing full justification based on your work in parts (a) and (b).