Find the critical numbers

1. Apr 1, 2013

frosty8688

1. Find the critical numbers of $F(x) = x^{\frac{4}{5}}(x-4)^{2}$

2. Power rule then chain rule

3. $F'(x) = \frac{4}{5}x^{\frac{-1}{5}} (x-4)^{2}*2(x-4)$ I know two critical numbers are 0 and 4 and I am having problems finding the third one.

2. Apr 1, 2013

Staff: Mentor

and product rule?
The first rule to use would be the product rule. It doesn't look to me like you used that rule.

3. Apr 1, 2013

HallsofIvy

Staff Emeritus
Another way to do this is to write
$$F(x)= x^{\frac{4}{5}}(x^2- 8x+ 16)= x^{\frac{14}{5}}- 8x^{\frac{9}{5}}+ 16x^{\frac{4}{5}}$$

4. Apr 1, 2013

frosty8688

That makes it easier to understand.

5. Apr 1, 2013

Staff: Mentor

Yes, but it would also be useful to use the product rule (correctly). The results should be the same for either method, but you might need to use some algebra to confirm that they are the same.

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