007A Sample Midterm 1, Problem 5

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

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

where  $h$  is the height in centimeters and  $m$  is the mass in kilograms. Calculate the rate of change of BSA with respect to height for a person of a constant mass of  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m=85.}   What is the rate at  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h=170}   and  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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?

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