MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let r(x)=cot(5x4+2x), defined on the interval −1<x<1.
(a) Compute r′(x).
(b) Solve r′(x)=0 on the open interval (−1,1) and list all critical points of r in this interval.
(c) Use either the First Derivative Test or the Second Derivative Test to classify each critical point found in part (b) as a local maximum, local minimum, or neither. Provide complete justification.
(d) Discuss the behavior of r as x approaches each endpoint from within the domain and explain how this behavior, together with your results from part (c), could be used to sketch a complete graph of r on [−1,1].