How do you find the stationary points on a curve?

Let y = f(x). The gradient of the tangent to the curve at a stationary point is equal to 0. To find an equation for the gradient of the curve, differentiate f(x) to get dy/dx. Because we are looking for stationary points, set the equation for dy/dx (the gradient) equal to 0. Rearrange to find the value(s) for x. Substitute the value(s) for x into the original equation for f(x) to find the corresponding y value(s). These are the stationary points on the curve.