The graph of a differentiable function contains the three points ,
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The graph of a differentiable function h contains the three points
C(1.9,4.5), D(2.0,4.8), and E(2.1,5.2).
(a) Compute the slope of the line through C and E and use it to estimate h′(2). Show your work.
(b) Compute the slope of the line through D and E. How does this value compare to your result in part (a)? Which estimate do you believe is closer to h′(2)? Explain your reasoning.
(c) Suppose additional graph information shows that h is concave down on the interval 1.9<x<2.1. Based on this fact, refine your answer to part (b) by indicating whether the estimate from part (a) is an overestimate or an underestimate of h′(2). Justify.