Thread: Find the critical numbers of a function

1. Find the critical numbers of a function

I know to find the critical numbers you'd find the first derivative and solve for where it is 0, but I just can't get the right answer for this one

f(x)= x^(1/5) - x^(-4/5)

2. Re: Find the critical numbers of a function

what did you get for the derivative? maybe the problem is in what you got.

3. Re: Find the critical numbers of a function

f'(x) = 1/[5x^(4/5)] + 4/[5x^(9/5)]

4. Re: Find the critical numbers of a function

what did you do when you set that equal to zero?

5. Re: Find the critical numbers of a function

First I factored out 1/5x^4/5

So I had: 1/[5x^(4/5)] x (1 + 4/x)

Then I set that to 0, but the first part is never zero so I just solved for where 1 + 4/x is 0 and got -4. Shouldn't that be the right answer?

6. Re: Find the critical numbers of a function

$\displaystyle f'(x)=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac {9}{5}}$

$\displaystyle 0=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac{9}{ 5}}$

$\displaystyle 0=\frac{1}{5x^{\frac{4}{5}}}(1+\frac{4}{x})$

What is the given answer? Because as far as I can tell, having checked, and having checked again, there's no problem with your work, unless I'm missing something.