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The atmospheric pressure of the air changes with height above sea level. The rate of change of the air pressure at a given height above sea level can be measured by the differentiable function
f(h), in psi per meter, where
h is measured in meters. What are the units of
f^(')(h) ?
meters
psi
meters / psi
psi / meter
meters
//psi^(2)
psi
// meter
^(2)

The atmospheric pressure of the air changes with height above sea level. The rate of change of the air pressure at a given height above sea level can be measured by the differentiable function $f(h)$ , in psi per meter, where $h$ is measured in meters. What are the units of $f^{\prime}(h)$ ? $\newline$ meters $\newline$ psi $\newline$ meters / psi $\newline$ psi / meter $\newline$ meters $/ \mathrm{psi}^{2}$ $\newline$ psi $/$ meter $^{2}$

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. The atmospheric pressure of the air changes with height above sea level. The rate of change of the air pressure at a given height above sea level can be measured by the differentiable function

f(h)

, in psi per meter, where

h

is measured in meters. What are the units of

f^{\prime}(h)

?

\newline

meters

\newline

psi

\newline

meters / psi

\newline

psi / meter

\newline

meters

/ \mathrm{psi}^{2}

\newline

psi

/

meter

^{2}

Understand $f(h)$ and $f'(h)$ : Understand the function $f(h)$ and its derivative $f'(h)$ . The function $f(h)$ represents the rate of change of air pressure with respect to height above sea level, and it is given in units of psi per meter. The derivative $f'(h)$ represents the rate of change of the function $f(h)$ with respect to height $h$ .
Determine derivative units: Determine the units of the derivative $f'(h)$ . $\newline$ Since $f(h)$ is measured in psi per meter, taking the derivative of $f(h)$ with respect to $h$ will give us the rate of change of the rate of change of air pressure with respect to height. This means we are looking at how the psi per meter changes as we move up each additional meter. Therefore, the units of $f'(h)$ will be the units of $f(h)$ divided by the units of $h$ .
Calculate $f'(h)$ units: Calculate the units of $f'(h)$ . The units of $f(h)$ are psi/meter, and the units of $h$ are meters. Dividing psi/meter by meters, we get: (\text{psi}/\text{meter}) / (\text{meters}) = \text{psi} / (\text{meter} * \text{meters}) = \text{psi} / \text{meter}^\(2

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