Chapter 1.8, Problem 3CYU

Let $f\left(t\right)$ be the temperature (in degrees Celsius) of a liquid at time $t$ (In hours).

The rate of temperature change at time $a$ has the value $f^{\prime }\left(a\right)$.Listed next are typical questions about $f(t)$ and its slope at various points. Match each question with the proper method of solution.

By how many degrees did the temperature rise during the first $6$ hours?

Methods of Solution

a. Compute $f\left(6\right)$.

b. Set $f\left(t\right)=6$ and solve for $t$.

c. Compute $\left[f\left(6\right)\text{- }f\left(0\right)\right]/6$.

d. Compute $f^{\prime }\left(6\right)$.

e. Find a value of $a$ for which $f\text{'}\left(a\right)=6$.

f. Compute $f\left(6\right)-f\left(0\right)$.