Quick Calculus question...?

Question

The following is a problem in my summer calculus packet...

There is a triangle symbol in the problem, and I don't know what that means. Since I don't have a triangle key on my keyboard, pretend that the "@" symbol is a triangle.

So, here is the problem:
Find f(x + @x) for f(x)=x^2 - 2x - 3

Answer 1

Wherever you see an "x" put an "x+∆x"
f(x) = x^2 -2x - 3, so
f(x+∆x) = (x+∆x)^2 - 2(x+∆x) -3
Now simplify.
= (x+∆x)(x+∆x) -2x -2∆x -3
= x^2 + 2∆x +(∆x)^2 -2x -2∆x -3
= x^2 + (∆x)^2 -2x -3

Answer 2

Hello...the little triangle is the math symbol for delta. Delta x means "small x" or a deviation around x.

f(x + delta x) = (x+delta x)^2 - 2(x+deltax) - 3

assuming delta x is small

x^2 +2xdeltax + deltax^2 - 2x - 2deltax -3

=x^2 + 2x deltax + 0 - 2x - 2 deltax -3

x^2 + 2(x deltax - x - deltax) - 3

note that if you let delta x to be small, you will get back the original equation.

Answer 3

The triangle is used to represent an increment

f(x+@x) = (x+@x)²-2(x+@x) -3
=x²+2x@x+@x²-2x-2@x - 3
=x²+@x²-2x-3

Answer 4

Δx is a small value of x
f ( x ) = x ² - 2 x - 3
f( x + Δ x ) = ( x + Δ x) ² - 2 ( x + Δx ) - 3