Question

Find the average rate of change for f(x)=9x^2+3 over the interval [x,x+h].

Answer 1

Answer:

$9h +18x$

Step-by-step explanation:

$\frac{f(x +h) -f(x)}{x+h -x} \\ \frac{9(x +h)^2 +3 -(9x^2 +3)}{h} \\ \frac{9(x^2 +2xh +h^2) +3 -9x^2 -3 }{h} \\ \frac{9x^2 +18xh +9h^2 +3 -9x^2 -3}{h} \\ \frac{9h^2 +18xh}{h} \\ 9h +18x$