MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A twice-differentiable function f is defined for −3≤x≤5. The graph of f′ consists of three straight-line segments that join the points (−3,−4), (0,2), (2,−1), and (5,3). You may assume these are the only critical points of f′ on the interval.
Using only the information provided about f′, respond to the following.
(a) Determine each open sub-interval of (−3,5) on which the graph of f is concave up and each sub-interval on which it is concave down.
(b) State the x-coordinate of every point of inflection of f in the domain −3<x<5.
(c) Explain how the behavior of f′ justifies your answers in parts (a) and (b).