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

Summary

For coffee with temperature $F(t) = 75 + 110e^{-0.05t}$ degrees Fahrenheit, a central difference with $h = 0.01$ at $t = 10$ estimates $F'(10)$. Round to three decimals, in degrees per minute.

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

The same coffee satisfies $F(t) = 75 + 110e^{-0.05t}$, with $F'(10) \approx -3.336$ degrees per minute. Which is greater, $F'(10)$ or $F'(20)$, and why?

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.

A tossed ball has velocity $v(t) = 16 - 32t$ ft/sec for $0 \le t \le 2$. The ball's velocity is greatest at $t = 0$.

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?

A car's value 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.

The same car also satisfies $h(70000) = 11100$ dollars. Using the best available estimate (a central difference), compute $h'(55000)$ in dollars per mile, rounded to three decimals.

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?