Question

Find the average rate of change of the functionf (x) = 3x2 + 4x – 5over the interval [0,h], where h is a positive real number.

Answer 1

The average rate of change of the function over the interval (0, h) is

`(f(h)-f(0))/(h-0)=(f(h)-f(0))/(h)`

Now,

`f(h)=3h^2+4h-5`

and

`f(0)=-5`

Therefore, the average rate of change is

`(3h^2+4h-5-5)/(h)=\textcolor{#FF7968}{(3h^2+4h-10)/(h).}`