Mathematics

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.