# Math Help - What are the critical numbers of this?

1. ## What are the critical numbers of this?

Hi can someone help me find the critical numbers of this function:

$f(x) = x^{8/9} - x^{17/9}$

I found the derivative to be:

$\frac{8}{9}x^{-1/9} - \frac{17}{9}x^{8/9}$

but then what?

Thanks!

2. Originally Posted by coldfire
Hi can someone help me find the critical numbers of this function:

$f(x) = x^{8/9} - x^{17/9}$

I found the derivative to be:

$\frac{8}{9}x^{-1/9} - \frac{17}{9}x^{8/9}$

but then what?

Thanks!
You're almost there!

Set $f'(x)=0$ and this will give you the stationary [critical] values. Also consider where $f'(x)$ fails to exist. You will also find critical points there as well.

--Chris

3. you must to make equal to zero the function derivative and to clear X

P.D: the answer is $\dfrac{8}{17}$