Optimisation with a Restricted Domain

For an absolute maximum or minimum on a closed interval, compare all admissible stationary values and both endpoints. A stationary point outside the physical domain cannot be used. Example For V(x)=x(10-x) with 0 <= x 3, V (x)=10-2x. The stationary value x=5 is outside the domain. V(0)=0, V(3)=21. Since V (x)>0 throughout the interior, the maximum is 21 at the endpoint x=3. When the constraint defines variables implicitly, differentiate that constraint before substituting the instantaneous condition. Use the chain rule to connect the derivative of the objective to the independent variable.