The basic algorithm for solving a standard maximization 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.
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.
In a previous Math-FAQ, we looked at the different parts of a parabola. Based on this information, you know that to find the x intercepts of a parabola we need to solve a quadratic equation. When we solve a quadratic equation to find the x intercepts of the graph, you might expect to always have solutions. But as the Math-FAQ below shows, this is not always the case.