Find maximum area of rectangle
Calculus
Level
3
A rectangle's bottom is at \(y=0\)
while its top corners are on the curve \(y=x{ (x-1) }^{ 2 }\) between \(x=0\) and \(x=1\). The maximum area of this rectangle can be expressed as
\[ \dfrac { a\sqrt { a } -b }{ c\sqrt { d } }\]
where \( a\) and \( d\) are prime numbers. What is the sum \(a+b+c+d?\)
(Don't count \( a\) twice)
by
Michael Mendrin