Example 5 from Algebra and Trigonometry, 3.3 Rates of Change and Behavior of Graphs

Finding the Average Rate of Change of a Force

The electrostatic force $F,$ measured in newtons, between two charged particles can be related to the distance between the particles $d,$ in centimeters, by the formula $F (d) = \frac{2}{d^{2}} .$ Find the average rate of change of force if the distance between the particles is increased from 2 cm to 6 cm.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We are computing the average rate of change of $F (d) = \frac{2}{d^{2}}$ on the interval $[2, 6] .$

$\begin{matrix} Average rate of change & = & \frac{F (6) - F (2)}{6 - 2} \\ = & \frac{\frac{2}{6^{2}} - \frac{2}{2^{2}}}{6 - 2} & Simplify . \\ = & \frac{\frac{2}{36} - \frac{2}{4}}{4} \\ = & \frac{- \frac{16}{36}}{4} & Combine numerator terms . \\ = & - \frac{1}{9} & Simplify \end{matrix}$
The average rate of change is $- \frac{1}{9}$ newton per centimeter.

How did it go?

Solution

Solution