Find the critical numbers of the function:
f(x) = x^(1/6)-x^(-5/6)

Question

Find the critical numbers of the function: 
f(x) = x^(1/6)-x^(-5/6)

anonymous · Answer

First, we differentiate

anonymous · Answer

f'(x) = 1/6x^(-5/6)+5/6x^(-11/6)

anonymous · Answer

is there supposed to be two x's or is one of them a y?

anonymous · Answer

yep, two x's.

anonymous · Answer

Just checking, the problem resembles a multivariable  calc prob. This is Calc 1 correct?

anonymous · Answer

Calc 1 indeed.

anonymous · Answer

I got the derivative, but it doesn't quite match up with yours. I can't tell, it looks a bit crunched up.

anonymous · Answer

$$(x+5)/6x^{11/6}$$ That is what I got.

anonymous · Answer

its a minus sign

anonymous · Answer

What is a minus sign?

anonymous · Answer

the exponents are fractions

anonymous · Answer

In thehe equation?

anonymous · Answer

Are you struggling with finding the derivative or finding the critical points?

anonymous · Answer

finding the points. I know to find the points, you set the derivative equal to zero and solve, but I just can't get it to work out without being undefined.

anonymous · Answer

and the answer, unfortunately, isn't undefined.

anonymous · Answer

Okay, so you found the derivative and set it equal to 0.

anonymous · Answer

Now it's just straight up algebra.

anonymous · Answer

there is no critical points

anonymous · Answer

I found one...? Am I wrong...?

anonymous · Answer

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