§1.5 Interpreting, estimating, and using the derivative (continued)

Summary

A ball tossed upward has velocity $v(t) = 16 - 32t$ ft/sec at time $t$ seconds. What is $v'(1)$ and what does it represent?

Coffee temperature is $F(t) = 75 + 110e^{-0.05t}$ degrees Fahrenheit. A central difference with $h = 0.01$ gives $F'(10) \approx -3.336$. This value means the coffee

A car's value is $h(m)$ dollars after $m$ miles. Data suggests the value curve is decreasing and bending upward as mileage grows. Which relation holds?

The same car satisfies $h(40000) = 15500$ and $h(55000) = 13200$ dollars. Compute the average rate of change of value on $[40000, 55000]$, in dollars per mile, rounded to three decimals.

For $F(t) = 75 + 110e^{-0.05t}$, a central difference with $h = 0.01$ at $t = 10$ gives a value. Round it to three decimals, degrees per minute.

If a drug dose of $q$ milliliters raises body temperature by $T = f(q)$ degrees Fahrenheit, then the sensitivity $s(q) = f'(q)$ is measured in degrees Fahrenheit per milliliter.