Mathematics

Problem

The table lists values of a differentiable function

f

$x$	$4.8$	$4.9$	$5.0$	$5.1$	$5.2$
$f(x)$	$22.99$	$24.02$	$25.05$	$26.10$	$27.17$

(a) Use the data at

x=4.9

and

x=5.1

to approximate

f'(5)

. (b) Use the data at

x=4.8

and

x=5.2

to approximate

f'(5)

. (c) Indicate which estimate in (a) or (b) is likely closer to the true value of

f'(5)

and give a brief reason.