1. ## Critical Points Help?

Hey guys,

I'm just having a bit of trouble with this one question. I'm trying to follow my teacher's notes but I don't have an example like it, so it's a little difficult for me.

Here's the question:

Find the critical numbers of the function. (Enter your answers as fractions.) F(x) = x4/5(x - 1)2

Here's what I've got so far:

f'(x) = 4/5x^-1/5 * (x-1)^2 - x^4/5
f'(x) = x^-1/5 (4/5(x-1)^2 -x^3/5)
f'(x) = x^-1/5 (4/5(x^2-2x+1) - x^3/5)
f'(x) = x^-1/5 (4/5x^2 - 13/5x^3/5 + 4/5) I combined the -8/5x with -x^3/5

I don't think I'm doing this right, however. A little bit of guidance would be appreciated?

2. Originally Posted by dark-ryder341
Hey guys,

I'm just having a bit of trouble with this one question. I'm trying to follow my teacher's notes but I don't have an example like it, so it's a little difficult for me.

Here's the question:

Find the critical numbers of the function. (Enter your answers as fractions.) F(x) = x4/5(x - 1)2

Here's what I've got so far:

f'(x) = 4/5x^-1/5 * (x-1)^2 - x^4/5
f'(x) = x^-1/5 (4/5(x-1)^2 -x^3/5)
f'(x) = x^-1/5 (4/5(x^2-2x+1) - x^3/5)
f'(x) = x^-1/5 (4/5x^2 - 13/5x^3/5 + 4/5) I combined the -8/5x with -x^3/5

I don't think I'm doing this right, however. A little bit of guidance would be appreciated?

$\displaystyle f(x) = x^{\frac{4}{5}} (x-1)^2$

product rule ...

$\displaystyle f'(x) = x^{\frac{4}{5}} \cdot 2(x-1) + (x-1)^2 \cdot \frac{4}{5}x^{-\frac{1}{5}}$

continue ...