MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
Consider the function f(x)=arccos(5x), whose domain is the set of all real numbers x satisfying ∣5x∣≤1.
(a) Compute f′(x) in simplest exact form.
(b) Determine the sign of f′(x) on the entire domain of f, and explain what this implies about whether f is increasing or decreasing.
(c) Decide whether f possesses any local extrema on its domain. Fully justify your conclusion using your work from part (b).