Finding Absolute Extrema: Solving for Critical Points in Rational Functions

[Julie H]

Homework Statement

(16x)/(x^2+4) for -5 (less than OR equal to) x (less than OR equal to) 5

Homework Equations

Set the derivative of the equation equal to 0, solve for x to find the critical points, then plug and check for validity.

The Attempt at a Solution

I used product rule for (16x)*(x^2+4)^-1

I got the derivative as
(-32x^2)/((x^2+4)^2) + (16/(x^2+4))
which I then set equal to 0.

I then made an attempt to solve for x, but got x^2(48x^2+256)=-256, which I'm very unsure of, and am also not sure how to solve.
Help is appreciated.

 

[justsof]

You have made an error while solving your equation. Try to write your original derivative as a single fraction and I hope it would be more clear then what to solve.
(Your final equation gives complex solutions which shouldn't be the case ;) )

 

[Julie H]

I see now! I really need to get more comfortable with the quotient rule. I think I end up running myself in circles too often because I try to use the product rule, and then can't alter the problem to look like it would, if I had used the quotient rule.

Thank you very much!