Question

Simplifique f(x+h) - f(x) / h (h diferente de 0) sendo f(x) igual 4x^2 + 4x

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{4\cdot(x+h)^2+4\cdot(x+h)-(4x^2+4x)}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{4\cdot(x^2+2xh+h^2)+4x+4h-4x^2-4x}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{4x^2+8xh+4h^2+4x+4h-4x^2-4x}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{4x^2-4x^2+4x-4x+8xh+4h^2+4h}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{8xh+4h+4h^2}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=\dfrac{h\cdot(8x+4+4h)}{h}$

$\sf \dfrac{f(x+h)-f(x)}{h}=8x+4+4h$