Question

For the Function f(x)=2x²−2x+6, simplify problems A) & B)

A) f(x+h)

B) (f(x+h)−f(x))/h

Please explain the steps you used.

Answer 1

A)

2(x+h)^2 -2(x+h) + 6
2(x^2 + 2 xh + h^2)-2x-2h +6
2x^2+4xh+2h^2-2x-2h+6

B)
[2x^2+4xh+2h^2-2x-2h+6-2x^2+2x-6]/h

[4xh+2h^2-2h]/h

4x + 2h - 2

note when h -->0 this becomes 4x-2