Question

me ajudem plz.

Identifique a unica opção correta.
Se f(X)=x²+2x e se h ∈ R , o valor de $\frac{f(X+h)-f(X)}{h}$ é:

a-2x+2+h
b-2x-2+h
c-2x-2-h
d-2x+2h²+h
e-2x-2h²+h
f-2x+2-h

obs:R = numeros reais.

Answer 1

$f(x)= x^{2} +2x$

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

$\dfrac{x^{2} +2xh+h^{2} +2x+2h-x^{2} -2x}{h}$

$\dfrac{2xh+h^{2} +2h }{h} =2x+h+2$

Letra a)

Answer 2

$\boxed{f(x)=x^2+2x}\\ \\ f(x+h)=(x+h)^2+2(x+h)=x^2+2hx+h^2+2x+2h\\ \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+2hx+h^2+2x+2h-x^2-2x}{h}=\frac{2hx+h^2+2h}{h}=\\ \\ \frac{h(2x+h+2)}{h}=2x+h+2$

LETRA A