A point on a graph at which the gradient of a tangent of a mathematical function changes sign. Where a gradient changes from a positive to a negative, the point represents a maximum point; where a gradient changes from a negative to a positive, the point represents a minimum. Turning points are also known as stationary points. Where the mathematical function $y=f(x)$ is known, the turning point can be obtained from the first derivative:

A maximum or minimum can be identified from the sign of its second derivative.