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

$\frac{f(h)-f(0)}{h-0}=\frac{f(h)-f(0)}{h}$

Now,

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

and

$f(0)=-5$

Therefore, the average rate of change is

$\frac{3h^2+4h-5-5}{h}=\textcolor{#FF7968}{\frac{3h^2+4h-10}{h}.}$