# Max and Min Values

1. Nov 16, 2005

OK, the professor did this problem for us as an example and i got lost somewhere in between. the problem was: find the critical points
f(x)= x^(4/5)*(x-4)^2

then he used the product rule to get

f '(x)= 4/5 x^(-1/5) *(x-4)^2 + x^(4/5) * 2(x-4) = 0

THEN, the part that threw me off was the next part where he said multiply both sides by 1/5....what did he mean by that? after that you get

4/5 (x-4)^2 + 2x(x-4) = 0 and so on...

my question is how and what did he do to get rid of the x^(-1/5) and the x^(4/5)???

Any help would be greatly appreciated

2. Nov 16, 2005

### NateTG

Multiply both sides by
$$x^{\frac{1}{5}}$$

3. Nov 16, 2005

### shmoe

He multiplied both sides by $$x^{1/5}$$, not 1/5.

4. Nov 16, 2005

### Hammie

Don't multiply by 1/5, try multiplying by x^(1/5). The whole idea is to turn the exponents into integers, and then you can use the usual methods to find the roots of the equation.

Last edited: Nov 16, 2005
5. Nov 16, 2005

### NonSequitur

He is not multiplying by 1/5, he is multiplying by x^(1/5). On the zero side, it of course goes away. On the other side, it distributes and x^(1/5)*x^(-1/5)=1 while x^(1/5)*x^(4/5)=x nicely killing off those pesky rational exponents. Good Luck

6. Nov 16, 2005

WOOHOOO!!!!! Thanks very much!

7. Nov 16, 2005

### HallsofIvy

"Never seen such unanimity of opinion before in my life"