To find Stationary Points, we differentiate the function and find the coordinates where the derivative is zero.

At the stationary point, the tangent to the point is horizontal.

There are mainly 3 kinds of Stationary Points: Max, Min and Point of Inflexion (There are non-stationary points of inflexion but it is not covered in detail in this topic). To determine the nature of the point (whether max/min/inflexion), we can use 2 methods:

1) 1st Derivative Test (Table method) OR
2) 2nd Derivative Test

Both methods has it's merits and demerits. Which one to use is dependent on the function you need to differentiate.

What are maximum and minimum points? Watch this video:
Minima, maxima and critical points:

http://www.khanacademy.org/math/calculus/derivative_applications/critical_points_graphing/v/minima--maxima-and-critical-points


What are points of inflexion? Watch this video:
Inflection points:

http://www.khanacademy.org/math/calculus/derivative_applications/critical_points_graphing/v/inflection-points



Derivation of Snell's Law: