find and simplify

Question

Find and simplify (f(x + h) − f(x))/h. for the function. f(x) = 2x² + 5x - 1

Answer 1

f(x+h) = 2(x+h)^2 + 5(x+h) - 1 =

2 (x^2 + 2xh+ h^2) + 5x + 5h - 1 =

2x^2 + 4xh + 2h^2 + 5x + 5h - 1 =

Subtracting f(x) from that gives 4xh + 2h^2 + 5h,

as 2x^2 +5x-1 cancels out

dividing that in bold above by h gives 4x + 2h + 5