[ 4xR^2 - 3x^3 = 0 \quad\Longrightarrow\quad x\bigl(4R^2 - 3x^2\bigr) = 0. ]
A ripple of impressed murmurs ran through the class. The professor nodded, his eyes twinkling. “Excellent,” he said. “You’ve illustrated perfectly how a multivariable problem can sometimes be reduced to one variable, and how the critical point tells us the shape of the optimal object. Well done, Maya.” [ 4xR^2 - 3x^3 = 0 \quad\Longrightarrow\quad x\bigl(4R^2
Maya solved for in terms of x :