# 009A Sample Midterm 2, Problem 4

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To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared) using the formula:

${\displaystyle {\text{BSA}}={\frac {\sqrt {hm}}{60}}}$

where  ${\displaystyle h}$  is the height in centimeters and  ${\displaystyle m}$  is the mass in kilograms. Calculate the rate of change of BSA with respect to height for a person of a constant mass of  ${\displaystyle m=85.}$  What is the rate at  ${\displaystyle h=170}$  and  ${\displaystyle h=190?}$  Express your results in the correct units. Does the BSA increase more rapidly with respect to height at lower or higher heights?