Pre calc question help please..?

Question

Let f(x)= 2x2-x+1 (2x is squared)

Find the difference quotient f(x+h) - f(x) / h , for each function

Answer 1

Well....... You've really only defined -one- function here. Namely
f(x) = 2x² - x +1 (unless you want to count 2x² and -x as functions)
But it really doesn't matter because you do them all the same way.
Let's just take 2x² - x + 1 to be the function f(x). Then you form
f(x+h) = 2(x+h)² - (x + h) -1 by replacing 'x' with 'x + h'. Now just do the indicated algebra and you're done.

Doug
EDIT: masterliang123 clearly doesn't know s.h.i.t from apple butter about Calculus or he (or she) wouldn't be quite so cavalier about first principles. Learn them well, they get to be fundamentally important later on ☺

Answer 2

Ahh, differentiation from first principles, how incredibly useless.

Anyway.

delta(y) / delta(x) = ( 2(x+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


Normally, you would take the limit h -> 0

leaving dy/dx = 4x -1

Which is what you get with the normal rules of differentiation.