How do I find the stationary points of a curve?

For a curve where y = f(x) the gradient of the curve is the derivative of this equation dy/dx. Stationary points of a curve occur when the gradient of the curve is zero. Hence find the expression for dy/dx and solve the equation:
dy/dx = 0
Once the x values which satisfy this equation are found the corresponding y values for each x value can be found by subbing the x values into the equation of the curve. You now have the full set of coordinates for the stationary points of the curve.
A possible extension would be to explain how the nature of the stationary points are found.