Thread: Using the difference quotient?

Hi! I'm new to Math Help Forums, so you'll have to forgive me if I don't do things correctly. I'm not quite sure how to post math icons either =/

So, I just have a basic difference quotient problem that was actually included in my review packet for the beginning of calculus one.

Question:
Evaluate the function at the given value of the independent variable.

F(x) = x^3
f(x+deltax)-f(x)/delta x

I got as far as plugging it in:
(x+delta x)^3-x^2/delta x

And, I know I'm supposed to simplify things out to get rid of the delta x on the bottom. I tried multiplying out the top and I got [x^2+x(delta x) +x(delta x) + (delta x)^2][x+delta x]/delta x. I'm not entirely sure if that's right, because the delta x's kind of confuse me. I wasn't quite sure how to continue.

Thanks!

EDIT: I forgot to mention! The back of the book states that the answer is 3x^2 + 3x(delta x)+(delta x)^2, where delta x does not equal zero. Thanks again!

It's mostly just an algebra problem in the numerator. Notice that



so:



If the terms are throwing you off, you can use instead. This is actually more common notation anyway.



Does this help?

Oh my gosh! I couldn't believe I forgot the difference of cubes! Thank you so much, that definitely makes more sense. I was trying to multiply everything out by hand instead of using a simple equation. Thank you!