Thread: 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)<sup>2

Would this be the simplified first derivative?</sup>

looks ok to me ...

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.

Let , so the equation becomes . Solve that for y then solve for x.

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.

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