Question

You have to plug in (x+h) for x but im stuck

Answer 1

Step-by-step explanation:

Given: $f(x) = 2x^2 - 4x + 5$

$f(x + h) = 2(x+h)^2 - 4(x + h) + 5$

$\:\:\:\:\:\:\:\:=2(x^2 + 2hx + h^2) - 4(x + h) + 5$

$\:\:\:\:\:\:\:\:= 2x^2 + 4hx + 2h^2 - 4x - 4h + 5$

$\dfrac{f(x + h) - f(x)}{h} = \dfrac{(2x^2 + 4hx + 2h^2 - 4x - 4h + 5) - (2x^2 - 4x + 5)}{h}$

$= \dfrac{4hx + 2h^2 - 4h}{h} = 4x - 4 + 2h$