Relative vs Absolute Extrema

Although a relative extrema may seem to be very similar to an absolute extrema, they are actually quite different. The term “relative” means compared to numbers nearby…so a relative extrema is either a bump or a dip on the function.

The term “absolute” means the most extreme on the entire function. An absolute extrema is the very highest or lowest point on the function. This may occur at a bump or a dip. They may also occur at the ends of the function if it is defined on a closed interval.

The MathFAQ below illustrates how to find these points on a function.

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Using the Simplex Method to Solve A Standard Maximization Problem

The basic algorithm for solving a standard minimization problem is covered in Section 4.3. This process, called the Simplex Method, uses matrices and row operations to gauge whether an objective function is maximized at corner points.

In the example below, I write out a standard maximization problem from an application and then solve it with the Simplex Method.

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