# Thread: Quotient Rule for first derivative help.

1. ## Quotient Rule for first derivative help.

I'm not sure about the result.

f(x)= (x3+x2)/(x2-4)

=(x2-4)(3x2+2x) - (x3+x2)(2x) / (x2-4)2

=(3x4+2x3-12x2-8x) - (2x4 + 2x3) / (x2-4)2

=(x4-12x2-8x) / (x2-4)2

Would this be the simplified first derivative?

2. ## Re: Quotient Rule for first derivative help.

looks ok to me ...

3. ## Re: Quotient Rule for first derivative help.

Thanks. Now for finding a possible critical value for increasing and decreasing intervals, I would take the numerator = 0. I'm having trouble on how I should go about that. I've looked up information on how to do critical values, but each has you factoring it down into (x-1) type terms. Meanwhile I have, x4-12x2-8x = 0. I can't factor out anything more than x.

4. ## Re: Quotient Rule for first derivative help.

Let $y= x^2$, so the equation becomes $y^2- 12y- 8= 0$. Solve that for y then solve $x^2= y$ for x.

5. ## Re: Quotient Rule for first derivative help.

Originally Posted by mettler
Thanks. Now for finding a possible critical value for increasing and decreasing intervals, I would take the numerator = 0. I'm having trouble on how I should go about that. I've looked up information on how to do critical values, but each has you factoring it down into (x-1) type terms. Meanwhile I have, x4-12x2-8x = 0. I can't factor out anything more than x.
$x(x^3-12x-8) = 0$

the cubic factor has three real roots, but none are rational ... you will most probably have to use technology to find them.