Given f(x)=2x^2+3x-1 determine the following: f(x+h)-f(x)/h

Question

Given f(x)=-2x² + 3x-1 determine the following:

f(x+h)-f(x)

h

I am having trouble with this and have many more similar questions so a step by step answer would be very helpful, thank you.

Answer 1

HI schedule a lesson to get more help.

sincerely,

Answer 2

Sure. This is always presented as the step before teaching students derivatives, as the limit as h goes to 0 is the derivative, or slope of the function at that point.

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

f(x) = 2x^2 + 3x - 1

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

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

4x + 3 + 2h