Imagine a flat-bottomed cylinderal container with a circular cross section of radius 4 in. a marble with radius 0<r<4 inches is placed in the bottom of the can. what is the radius of the bottom that requires the most water to cover it. (include first or second derivative test to prove it)

something wrong with the solution I posted a few hours ago?

http://www.jiskha.com/display.cgi?id=1429156887