Solve the Problem

Essay

Solve the problem.
- $$\text { Let } c ( x ) = t \left( p _ { 0 } - p \right) p ^ { 3 } \text { where } t \text { and } p _ { 0 } \text { are constants. Show that } c ( x ) \text { is greatest when } p = \frac { 3 } { 4 } p _ { 0 } \text {. }$$