Wow. I need help. Find f( x + Δx ) for f(x) = x² - 2x - 3. I don't remember how to do this at all.?

Answer 1

To break it down a wee bit more, f(X + dX), where dX is a small bit, or a small change

f(X) = X^2 - 2X - 3, and just put in (X +dX) instead of X

so f(X + dX) = (X +dX)^2 - 2(X+ dX) - 3

which is X^2 + 2XdX + dX^2 - 2X - 2dX - 3,

which is as simplified as you can make it.

Answer 2

Plug in x = x + Δx . That's

x² +2xΔx +Δx² -2x -2Δx -3

Answer 3

Replace x by x + dx to get f ( x + dx ) from f ( x )

Thus, f ( x + dx) = ( x + dx )^2 - 2 ( x + dx ) -3
= x^2 + 2x (dx) + (dx)^2 -2x -2dx -3
= x^2 + 2 ( x - 1 )dx + (dx)^2 - 2x - 3