If I have the equation of a curve, how do I find its stationary points?

A stationary point is where the gradient of a curve momentarily stops changing.Let's take the example that we want to find the stationary points of the curve y=2x^5 - 5x^2. Find the derivative of the equation using the standard differentiation method. 2x^5 - 5x^2 would derive to 10x^4 - 10x. Then find the second derivative, by differentiating your first derivative in the same way. 10x^4 - 10x would become 40x^3 - 10. To find the stationary points, set the second derivative equal to 0, so in our example 40x^3 -10 = 0. Using this new equation, solve for x. In our case, solving for x gives us x^3=0.25 and therefore x=0.630 (3.s.f). If the question asks for it, you may need to find the y-coordinate by substituting the x-value back into the original equation- in this case we get y=1.789 (3.s.f).