The derivative of a twice-differentiable function is described as follows for : • On ,
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The derivative of a twice-differentiable function f is described as follows for −1≤x≤6:
• On −1≤x<1, f′(x)=3.
• On 1≤x<3, f′(x) decreases linearly from 3 to −1.
• At x=3, f′ is undefined because f′ has a removable discontinuity; assume f itself remains continuous there.
• On 3<x≤6, f′(x)=−1.
Suppose f(−1)=4.
Answer the prompts below.
(a) Compute f(1) and f(3).
(b) Determine all intervals on which f is strictly increasing and all intervals on which it is strictly decreasing. Justify fully.
(c) Explain whether f possesses a relative extremum at x=3. Support your conclusion with appropriate reasoning.