How do I find a stationary point on a curve and work out if it is a maximum or minimum point?

At any stationary point, the gradient of a line is zero.
Therefore dy/dx = 0. If we differentiate the equation of the line, and solve this expression we can find the coordinates of the stationary point.
If we differentiate again, we find f''(x):If f''(x) < 0, the point is a maximum;If f''(x) > 0, the point is a minimum.
I will talk through an example on the interactive whiteboard.