Geometry of Functions V: Maximum and Minimum

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Lesson Summary: 
We provide the definition and graphical intuition behind the concepts of maximum and minimum. A maximum is the top of a hill and a minimum is the bottom of a valley.
Lesson Inputs: 
Geometry of Functions IV: Using Derivatives To Identify Increasing and Decreasing Functions
Lesson Outputs: 
Geometry of Functions VI: Critical Points

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Lesson: 

Think of maximum as the top of a hill and minimum as the bottom of a valley. A picture tells it all:

Maximum and Minimum

The exact definitions are as follows:

Maximum
A function $f(x)$ has a maximum at point $e$ if and only if <Sign in to see all the formulas> for all $x$ close to $e$.

and

Minimum
A function $f(x)$ has a minimum at point $e$ if and only if <Sign in to see all the formulas> for all $x$ close to $e$.