Question

Simplifique f(x+h) - f(x)/h sendo f(x) igual a x^3 + x^2 - x

Answer 1

Boa noite!

$\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^3+(x+h)^2-(x+h)-(x^3+x^2-x)}{h}\\\dfrac{x^3+3x^2h+3xh^2+h^3+x^2+2xh+h^2-x-h-x^3-x^2+x}{h}\\\dfrac{3x^2h+3xh^2+h^3+2xh+h^2-h}{h}=3x^2+2x-1+3xh+h^2+h$

Espero ter ajudado!