Question

How do you find the average rate of change of the function `y= 4x^2` over the interval [1, 5]?

Answer 1

24

Explanation:

the `color(blue)"average rate of change"` of y = f(x)over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the `color(blue)"secant line"` connecting the 2 points.

To calculate the average rate of change between the 2 points.

`color(red)(|bar(ul(color(white)(a/a)color(black)((f(b)-f(a))/(b-a))color(white)(a/a)|)))`

`f(5)=4(5)^2=100" and " f(1)=4(1)^2=4`

The average rate of change between (1 ,4) and (5 ,100) is

`(100-4)/(5-1)=96/4=24`

This means that the average of the slopes of lines tangent to the graph of f(x) between (1 ,4) and (5 ,100) is 24.