Activity 1.5.3 — Active Calculus

A potato is placed in an oven whose temperature is 350 degrees Fahrenheit, and the potato's temperature $F$ (in degrees Fahrenheit) is recorded in the following table. Time $t$ is measured in minutes.

Potato temperature data in degrees Fahrenheit.
$t$	$0$	$10$	$20$	$30$	$40$	$50$	$60$
$F(t)$	$65$	$94.7$	$141.7$	$167.6$	$182.4$	$197.9$	$209.3$

Use a central difference to estimate the instantaneous rate of change of the potato's temperature at $t= 20$ . Include units on your answer.
Use a central difference to estimate the instantaneous rate of change of the potato's temperature at $t= 40$ . Include units on your answer.
Without doing any calculation, which do you expect to be greater: $F'(50)$ or $F'(60)$ ? Why?
Suppose we know that $F(46) = 192.5$ and $F'(46) = 1.39$ . What are the respective units on these two quantities? What do you expect the temperature of the potato to be when $t = 47$ ? when $t = 48$ ? Why?
Write a couple of careful sentences that describe the behavior of the temperature of the potato on the time interval $[10,40]$ , as well as the behavior of the instantaneous rate of change of the potato's temperature on the same time interval.

Boelkins, Active Calculus, §1.5 Interpreting, estimating, and using the derivative, Activity 1.5.3

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