Step-by-step explanation:
Given: [tex]f(x) = 2x^2 - 4x + 5[/tex]
[tex]f(x + h) = 2(x+h)^2 - 4(x + h) + 5[/tex]
[tex]\:\:\:\:\:\:\:\:=2(x^2 + 2hx + h^2) - 4(x + h) + 5[/tex]
[tex]\:\:\:\:\:\:\:\:= 2x^2 + 4hx + 2h^2 - 4x - 4h + 5[/tex]
[tex]\dfrac{f(x + h) - f(x)}{h} = \dfrac{(2x^2 + 4hx + 2h^2 - 4x - 4h + 5) - (2x^2 - 4x + 5)}{h}[/tex]
[tex]= \dfrac{4hx + 2h^2 - 4h}{h} = 4x - 4 + 2h[/tex]
