I'm trying to find the critical point for f(x)=2x^2-1000*sqrt(x). However, I do already know the answer, but I have no idea how it is the answer. I've tried to work it out multiple times, but I keep going in the same loop. Here's my work on paper: http://puu.sh/BXjHY/dc18f00104.jpg
At the end of my work, when I'm faced with 125 = x^(3/2), I get an answer above a thousand, yet if i were to flip the exponential fraction so that the equation would then be 125 = x^(2/3), I get 25. I can't figure out where that x^(2/3) would come from!
Any help would be greatly appreciated!
$$125 = x^{3/2} \implies 125^{2/3} = x^{(3/2)(2/3)} =x$$
That is $$x= 125 ^{2/3} = 5^2 = 25 $$