#### Question

The fastest drag racers can reach a speed of 330 mi/hr over a quarter-mile strip in 4.45 seconds (from a standing start). Complete the following sentence about such a drag racer: At some point during the race, the maximum acceleration of the drag racer is at least ____ mi/hr/s.

#### Solution

Verified#### Step 1

1 of 2$\textbf{Mean Value Theorem}$: if $f$ is a continuous function on the closed interval $[a, b]$, and differentiable on the open interval $(a, b)$, then there exists a point $c$ in $(a, b)$ such that:

$\begin{gather*} f'(c)=\dfrac{f(b)-f(a)}{b-a} \end{gather*}$

We are given that $f(0)=0$ and $f(4.45)=330$. Therefore,

$\begin{gather*} f'(c)=\dfrac{330-0}{4.45-0}\\ f'(c)=\dfrac{330}{4.45}\\ f'(c)\approx74.16 \text{ mi/hr/s} \end{gather*}$

At some point during the race, the maximum acceleration of the drag racer is at least 74.16 mi/hr/s.