F (x) = 2x^2 + x - 1

Find f (x+h) - f (x) / h

[f (x+h) - f (x) ] / h = [2 (x+h) ^2 + (x+h) - 1 - (2x^2 + x - 1) ] / h =

= [ 2 (x^2 + 2xh + h^2) + x + h - 1 - 2x^2 - x + 1] / h =

= [2x^2 + 4xh + 2h^2 + x + h - 1 - 2x^2 - x + 1] / h =

= [4xh + 2h^2 + h] / h = 4x + 2h + 1

Answer: 4x + 2h + 1

Do you want the limit of that when h → 0? It is 4x + 2 (0) + 1 = 4x + 0 + 1 = 4x + 1