given the function f(x) = 2x^2-3x-1 simplify f((x+h)-f(x))/h

Answer 1

f(x) = 2x^2-3x-1
f(x+h) = 2(x+h)^2 - 3(x+h) - 1
= 2(x^2 + 2xh + h^2) - 3x - 3h - 1
= 2x^2 + 4xh + 2h^2 - 3x - 3h - 1

then : f((x+h)-f(x))/h
= ( 2x^2 + 4xh + 2h^2 - 3x - 3h - 1 - (2x^2-3x-1) )
= ( 4xh + 2h^2 - 3h)/h
= 4x - 3, h ≠ 0

Answer 2

Thank you.

Answer 3

( 4xh + 2h^2 - 3h)/h = 4x-3+2h