This should be in Calculus.

The first derivative determines the stationary points (they occur when the derivative is 0).

The second derivative determines whether it is maximum or a minimum.

If the second derivative is negative at the stationary point, you have a maximum.

If the second derivative is positive at the stationary point, you have a minimum.

If the second derivative is 0 at the stationary point, you may or may not have a stationary point of inflexion.