Table 3 shows selected values of the first derivative of a differentiable function
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Table 3 shows selected values of the first derivative h′ of a differentiable function h. The value of h′(1) was not recorded.
Table 3. Incomplete data for h′(x)
x −2 −1 0 1 2 3
h'(x) 4 2 0 ? −1 −3
Answer the following. All reasoning and intermediate work must be included.
(a) Provide a numerical estimate for h′(1). State and justify the method you used to obtain the estimate from the surrounding data.
(b) Using your completed table, determine on which open intervals in the domain shown the graph of h is concave up and on which intervals it is concave down.
(c) Discuss how sensitive the concavity classification in part (b) is to the specific estimate you chose for h′(1). Support your discussion with quantitative reasoning.