Question

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

Answer 1

`0`

Explanation:

The average rate of change of a function on the interval `[a,b]`, is given by:

`(f(b)-f(a))/(b-a)`

`f(x)=sinx`

For `[0,pi]`

`:.`

`(f(pi)-f(0))/(pi-0)`

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

The average rate of change is just the gradient of a secant line connecting the two points. It can be seen from the graph that in this case the line is horizontal .i.e. gradient = zero.

GRAPH: