Could you please help me out with this exercise?

Question

For the function , evaluate and fully simplify each of the following. =     =  

Answer 1

f(x) = 5x² - 3x + 3

First we calculate f(x + h)

f(x + h) = 5(x + h)² - 3(x + h) + 3

We simplify

f(x + h) = 5x² + 10hx + 5h² - 3x - 3h + 3.

We rewrite as

f(x + h) = (5x² - 3x + 3) + 10hx + 5h² - 3h + 3.

The bracket is equal to f(x). Hence

f(x + h) = f(x) + 10hx + 5h² - 3h or f(x + h) - f(x) = 10hx + 5h² - 3h .