3.3 Rates of change and behavior of graphs  (Page 2/15)

In 2007, the price of gasoline was $2.84. In 2009, the cost was $2.41. The average rate of change is

At $t=-1,$ [link] shows $g\left(\mathrm{-1}\right)=4.$ At $t=2,$ the graph shows $g\left(2\right)=1.$

The horizontal change $\text{Δ}t=3$ is shown by the red arrow, and the vertical change $\text{Δ}g(t)=-3$ is shown by the turquoise arrow. The average rate of change is shown by the slope of the orange line segment. The output changes by –3 while the input changes by 3, giving an average rate of change of

Here, the average speed is the average rate of change. She traveled 282 miles in 6 hours.

The average speed is 47 miles per hour.

We can start by computing the function values at each endpoint of the interval.

Now we compute the average rate of change.

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

The average rate of change is $-\frac{1}{9}$ newton per centimeter.

We use the average rate of change formula.

This result tells us the average rate of change in terms of $a$ between $t=0$ and any other point $t=a.$ For example, on the interval $[0,5],$ the average rate of change would be $5+3=8.$