Question

Seja f(x)=x-x^2 , encontre o valor de [f(x+h)-f(x)]/h, para h diferente de 0.

Answer 1

$\frac{f(x+h)-f(x)}{h}\\\\\\\frac{\left((x+h)-(x+h)^2~-~(x-x^2)\right)}{h}\\\\\\\frac{\left((x+h)-(x^2+2xh+h^2)~-~(x-x^2)\right)}{h}\\\\\\\frac{x+h-x^2-2xh-h^2-x+x^2}{h}\\\\\\\frac{h-2xh-h^2}{h}\\\\\\\frac{h.(1-2x-h)}{h}\\\\\\\boxed{1-2x-h}$

Reposta:  1 - 2x - h