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	Mathematics-Online lexicon:
	Extreme Value Problems

• circumference
• distance
• surface area
• etc.

1.)

Arrange an objective function.

2.)

Determine the domain of the objective function.

3.)

Differentiate the objective function two times.

4.)

Set the first derivative equal zero as like the culation of extrema.

5.)

Insert the solutions in the second derivative, to detect whether it is a minimum or a maximum.

Finally control if it is a relative or an absolute maximum (minimum):

6a)

Calculate the values of the objective function at the boundary of the domain.

6b)

Calculate the values of the objective function at the maximum (minimum).

It is an absolute maximum (minimum), if there is no value from 6a) exceeds (undershoots) a value of 6b), otherwise it is a relative maximum (minimum).

Example:

• Extreme Value Problem