Finding maxima and minima of a function
If a function has a local minimum or maximum value then the rate of change at that point must be 0.
Using calculus we can find maximum and minimum values by setting the derivative of the function to 0.
How do you tell which it is? One way is to look at the value of the derivative a short distance below and above the point in question. If the derivative is negative below and positive above then it is a minimum point. If it is positive below and negative above then it is a maximum point.
There is another possibility though - what if the derivative is positive immediately below and also positive above. Then you have a point of inflexion. For example, y=x3 has one at x=0.
Exercises:
[diffmaxminfnxl]