How do i know where a stationary point is and what type of stationary point it is?

Stationary points are points on a curve where the gradient is zero. There are three types of stationary point maximum, minimum and point of inflexion. (will draw diagrams). They can be found by differentiating (finding dy/dx) the curve and equating it to zero. When determining the type of stationary point we look to the second derivative, differentiate the curve again and compute its value at the stationary point. If the value is positive then it is a minimum point. If the value is negative then it is a maximum point. If the value is zero it could be either a minimum, maximum or a point of inflexion, in this case we look at the gradient (dy/dx) at either side of the stationary point (will explain in more detail using diagrams).