# [SOLVED] Isolate for x

• Apr 5th 2008, 03:50 PM
NAPA55
[SOLVED] Isolate for x
This is some pretty freaky algebra I've got here... hopefully my derivative is right lol

I need to set C'(x) = 0 and isolate for x (it's an optimization).

0 = [(1000x - 200000) / (√(x2 - 400x + 44900)] + 500

What happened to the HTML and MATH code?
• Apr 5th 2008, 03:57 PM
mr fantastic
Quote:

Originally Posted by NAPA55 and edited by Mr F
This is some pretty freaky algebra I've got here... hopefully my derivative is right lol

I need to set C'(x) = 0 and isolate for x (it's an optimization).

$\displaystyle C'(x) = \frac{1000(x-200)}{\sqrt{x^2-400x+44900}}+500$

$\displaystyle 0 = \frac{1000(x-200)}{\sqrt{x^2-400x+44900}}+500$

$\displaystyle \Rightarrow -1 = \frac{2(x-200)}{\sqrt{x^2-400x+44900}}$

$\displaystyle \Rightarrow - \sqrt{x^2-400x+44900} = 2(x-200)$

Now square both sides and solve the resulting quadratic equation.
• Apr 5th 2008, 04:25 PM
NAPA55
Perfect, thanks!

I subbed in my values back into my optimization problem and my answer seems correct!