Max/min problem: f(x) = (x)(sqrt of (2 - x))

[yummymummy1713]

How would I go about finding the max and/or min of f(x) = (x)(squareroot of(2 - x))? I know to graph it in my calc, but is that all I should do and then hit the calculate max/min button...? But the function looks like a hook, so it can't have a minimum...right?

Thanks. Normally I would get this, but I have confuzzled myself.

 

[galactus]

Actually, you need to graph \(\displaystyle {-}x\sqrt{2-x}\), too, along with \(\displaystyle x\sqrt{2-x}\)

 

[yummymummy1713]

ok so would I just say that my max and min are (1.33, 1.09) and (1.33, -1.09) respectively? or is there more? because that just seems too easy and my teacher doesn't give too easy problems

 

[galactus]

That's about all there is to it. \(\displaystyle \L\\\left(\frac{4}{3},\pm\frac{4\sqrt{6}}{9}\right)\)