Chapter 4.8, Problem 20ES

Use the result of Exercise 18 in these exercises.

At $11\text{ A}\text{.M}\text{.}$ on a certain morning the outside temperature was $76\text{°F}$ . At $11\text{ P}\text{.M}\text{.}$ that evening it had dropped to $52°\text{F}$ .

(a) Show that at some instant during this period the temperature was decreasing at the rate of $2°\text{F/h}$ .

(b) Suppose that you know the temperature reached a high of $88°\text{F}$ sometime between $11\text{ A}\text{.M}\text{.}$ and $11\text{ P}\text{.M}\text{.}$ Show that at some instant during this period the temperature was decreasing at a rate greater than $3°\text{F/h}$ .