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| Finding the Minimum and Maximum of a Function |
Finding the Minimum and Maximum of a Function
Finding the maximum or minimum of a function is an important concept in mathematics, and can be applied to many other areas of Science and Engineering for concepts such as Physics or Optimization in Statistics and Machine Learning. A function has a relative (local) maximum or minimum at any point where it's rate of change is 0.
This is easy to see from the above example, showing a function with a local maximum and local minimum where the rate of change is 0. Formally, the rate of change of a mathematical function is called the derivative. Calculating the derivative of a function gives the instantaneous rate of change at any point in the function.
Since a local maximum or minimum is found when the rate of change is zero, to the find the maximum or minimum of a function, one simply has to calculate the derivative and set it equal to 0.
An absolute maximum or minimum is the highest or lowest point in an entire function.