What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?

A stationary point simply means a point in a curve where the gradient is equal to 0.For example, in the June 2015 C3 Paper it is asked:Find the exact values of the coordinates of the stationary points of the curve.The curve function is f(x) = 6lnx + x^2 - 8x + 3 To calculate the gradient, we need to differentiate, as the gradient can also be represented as the change in y in respect to the change in x, or in other words dy/dx.dy/dx = 6/x + 2x - 8Where dy/dx = 0 is where the stationary point will be, 6/x + 2x - 8 = 0; multiplying all by x will give a quadratic: 6 + 2x^2 - 8x = 0, which can then be factorised: (2x-2)(x-3) = 0Solving this x = 1 or x= 3. Calculating y from the original function gives y = -4 and y = 6ln3 - 12, giving the co-ordinates (1,-4) and (3,6ln3 - 12)These questions are often worth a substantial amount of marks.