Question

For the function `f(x) = 1+3x-x^2`, what is `f(a+h) - f(a)`?

Answer 1

`= 3 h - 2ah -h^2 or h(3-2a-h)`

Explanation:

`f(a +h) -f(a)= [1+3 (a + h)-(a+h)^2)] - [1+3 a-a^2]`

`=1+3 a +3 h-(a^2+2ah+h^2)-1-3 a +a^2`

`=cancel 1+cancel (3 a) +3 h - cancel (a^2) -2ah -h^2-cancel 1- cancel (3 a) + cancel (a^2)`

`= 3 h - 2ah -h^2 or h(3-2a-h)`