1. ## finding minimum

$\displaystyle AC=\frac{TC}{x}=\frac{2000}{x}+20+\frac{10}{\sqrt{ x}}$
So i have to show that there is no minimum.

thus i have to differentiate the function, which apparently gives this

$\displaystyle \frac{dAC}{dx}=AC'= -\frac{2000}{x^2}-\frac{5}{\sqrt[3]{}x^3}$

I don't know how they got that answer , can someone please explain?

2. Originally Posted by el123
$\displaystyle AC=\frac{TC}{x}=\frac{2000}{x}+20+\frac{10}{\sqrt{ x}}$
So i have to show that there is no minimum.

thus i have to differentiate the function, which apparently gives this

$\displaystyle \frac{dAC}{dx}=AC'= -\frac{2000}{x^2}-\frac{5}{\sqrt[3]{}x^3}$

I don't know how they got that answer , can someone please explain?

$\displaystyle AC = \frac{2000}{x}+20+\frac{10}{\sqrt{x}}$

$\displaystyle AC = 2000x^{-1} + 20 + 10x^{-\frac{1}{2}}$

use the power rule ...

$\displaystyle AC' = -2000x^{-2} - 5x^{-\frac{3}{2}}$

rewrite ...

$\displaystyle AC' = -\frac{2000}{x^2}-\frac{5}{\textcolor{red}{\sqrt{x^3}}}$

note there is no "cube" root in the denominator of the last term.

3. Thanks.