A differentiable function is defined for all real numbers
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A differentiable function g is defined for all real numbers. Table 1 lists selected values of its first derivative g′.
Table 1. Values of g′(x)
x −3 −2 −1 0 1 2 3
g'(x) −4 −2 −1 −0.5 0 −0.5 −1
Answer the following. Use complete sentences and provide clear justification based on the numerical evidence in Table 1.
(a) Determine the open intervals on the domain shown where the graph of g is concave up and where it is concave down.
(b) Identify every x–coordinate in the table that is a candidate for a point of inflection of g, and justify your selection by referencing the behavior of g′.
(c) Explain in practical terms how the change in concavity you found in part (b) affects the overall shape of the graph of g. Your explanation should refer to the increases and decreases observed in g′. No sketch is required.