Question 115136
*[Tex \LARGE f\left(x+h\right)=\frac{{f\left( {x + h } \right) - f\left( x \right)}}{h }] Start with the given formula




*[Tex \LARGE f\left(x+h\right)=\frac{(x+h)^2 -\left(x^2\right)}{h }] Plug in {{{f(x+h)=(x+h)^2}}} and {{{f(x)=x^2}}}



*[Tex \LARGE f\left(x+h\right)=\frac{\left[x^2+2hx+h^2\right] -\left(x^2\right)}{h }] Foil/Expand {{{(x+h)^2}}}




*[Tex \LARGE f\left(x+h\right)=\frac{2hx+h^2}{h }] Combine like terms (i.e. combine {{{(x^2)-(x^2)}}} to get 0)


*[Tex \LARGE f\left(x+h\right)=\frac{h\left(2x+h\right)}{h }] Factor out an h


*[Tex \LARGE f\left(x+h\right)=\frac{2x+h}{1}] Divide {{{h/h}}} to get 1


*[Tex \LARGE f\left(x+h\right)=2x+h] Simplify