Definition
A Maximum is the coordinates of the location on a function where the y value is at it's highest. It is found by:
- Determining the derivative (gradient function) of the original function.
- Setting the derivative to equal zero. Zero is the gradient of all maximums, minimums and points of inflection.
- Solve for x value.
- Substitute x value into original function to find y value.
- Determine gradient on either side of the maximum by randomly selecting an x value lower and an x value higher. Substitute these two values into the derivative to find the gradient. If the gradient on the left is positive and the gradient on the right is negative, the stationary point is a maximum.
Class Example
Find the stationary point between x=-1 and x=1 for the function and determine its nature.