Question

See attached picture

Answer 1

Answer:

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

Step-by-step explanation:

Given

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

Required

Determine: $\frac{f(x+h)-f(x)}{h}$

First, we calculate f(x + h)

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

$f(x+h) = (x+h)^2+2$

$f(x+h) = x^2+2xh+h^2+2$

So, we have:

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

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

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

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