Solve the Problem

question 208

Essay

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

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Definitions:

Self-Respect

The regard for one’s own standing or position, reflected in behavior showing that one values their own dignity and worth.

Individual Responsibility

The obligation of an individual to act ethically and sensibly on their own accord without external pressure.

Lobotomies

A now largely obsolete surgical procedure intended to treat mental illnesses by severing connections in the brain's prefrontal lobe.

Psychological Disorders

Mental disorders characterized by patterns of behavior or thoughts that are unhealthy and disruptive.