Question

What is the average rate of change of the function `f(x)=sin x` on the interval [0, pi/2]?

Answer 1

`2/pi`

Explanation:

The average rate of change of a function `f(x)` on the interval `[a,b]` is equivalent to the slope of the secant line connecting those two points on the function, that is:

`"average rate of change"=(f(b)-f(a))/(b-a)`

So, the average rate of change of `f(x)=sinx` on `[0,pi/2]` is

`(sin(pi/2)-sin(0))/(pi/2-0)=(1-0)/(pi/2)=1/(pi/2)=2/pi`