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# Rate of Change Approximation: Reasonable Number

APCALC-QYEYJN

Fast filing Frank's job is to file files for Files Inc. The company recently ran a report and found the following data about Frank, where $t$ is in hours and $f$ is the number of files that Frank has filed during his work day. Also, $f$ is twice differentiable function.

$t$ 0 2 4 6 8
$f'$ 84 73 68 52 41

Because Frank tires as he works, the rate that Frank files decreases as the day goes on. Which of the following is a reasonable number of files that Frank could have filed during his workday between $0\le t\le 8$?

A

$318$ files

B

$468$ files

C

$502$ files

D

$554$ files