Find the stationary point of the curve y = -2x^2 + 4x.

Firstly, since we have a negative coefficient of x^2, we know we are looking for a maximum point. It is also always helpful to draw a sketch so you know what's going on. Whiteboard sketch. Now to find the stationary point of a function, we are looking for the point where the gradient is 0 (flat), and to do this we need to find the gradient function by differentiating the function and equating it to 0. So in this case, differentiating term by term, we multiply the coefficient of x^2 by its power and then reduce the power. So -2 x 2 = -4 which is our new coefficient, and our new power of x is 2 - 2 = 1. So we have -4x. Now to differentiate 4x, we multiply the coefficient 4 by the power 1 and then reduce the power of x from 1 to 0, so we have 4. Then our gradient function is dy/dx = -4x + 4, where the dy/dx is just notation we don't need to worry about right now. So, equating this to 0 we simply solve -4x + 4 = 0, and see that x = 1. Finally we just need our y-coordinate, so we plug in our value of x = 1 into the original function and see that y = 2. So the stationary point of the curve is (1,2).