Question

Find the average rate of change on the interval [-3,3] for the given function

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's use those two points off the curve in order to get it, check the picture below.

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{1}{3 +3}\implies {\LARGE \begin{array}{llll} \cfrac{1}{6} \end{array}}`