Question

PLEASE ANSWER ASAP 25 POINTS + BEST GETS BRAINLIEST

Recall that the difference quotient of a function f(x) is defined as f(x+h)−f(x)h, where we assume h is not 0.

Find the difference quotient of the function f(x)=x2
. Simplify your answer.

Answer 1

$f(x)=x^2\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^2-x^2}{h}\\\\=\dfrac{x^2+2xh+h^2-x^2}{h}=\dfrac{2xh+h^2}{h}\\\\=\dfrac{h(2x+h)}{h}=\boxed{2x+h}$

Used:
(a + b)² = a² + 2ab + b²