Exercise 8 — Active Calculus

A potato is placed in an oven, and the potato's temperature $F$ (in degrees Fahrenheit) at various points in time is taken and recorded in the following table. Time $t$ is measured in minutes.

Temperature data for the potato.
$t$	$0$	$10$	$20$	$30$	$40$	$50$	$60$
$F(t)$	$65$	$94.7$	$141.7$	$167.6$	$182.4$	$197.9$	$209.3$

Use a central difference to estimate $F'(30)$ . Use this estimate as needed in subsequent questions.
Find the local linearization $y = L(t)$ to the function $y = F(t)$ at the point where $a = 30$ .
Determine an estimate for $F(33)$ by employing the local linearization.
Do you think your estimate in (c) is too large or too small? Why?

Boelkins, Active Calculus, §1.8 The tangent line approximation, Exercise 8

AI Tutor