A function is strictly increasing in the closed interval [a , b], if the derivative of the function is positive at every point in the open interval (a , b).

A function is strictly decreasing in the closed interval [a , b], if the derivative of the function is negative at every point in the open interval (a , b).

A function is constant in the closed interval [a , b], if the derivative of the function is zero at every point in the open interval (a , b).