Question

Find the average rate of change of each function on the interval specified in simplest form. Do not type your answer in factored form and do not type any spaces between characters. g(x)=3x^2-2 on the interval [x,x+h]The average rate of change is Answer

Answer 1

The average rate of change formula is

$A=\frac{f(b)-f(a)}{b-a}$

Substitute the values in the formula

$A=\frac{3(x+h)^2-2-3x^2+2}{x+h-x}$$A=\frac{3(x^2+h^2+2xh)-3x^2}{h}$$A=\frac{h^2+2xh}{h}=\frac{h(h+2x)}{h}=h+2x$

Hence the average rate of change is 2x+h.