Problem #PRU-97832

Problems Calculus Functions of one variable. Continuity Continuous functions (general properties)

Problem

f(x) is an increasing function defined on the interval [0,1]. It is known that the range of its values belongs to the interval [0,1]. Prove that, for any natural N, the graph of the function can be covered by N rectangles whose sides are parallel to the coordinate axes so that the area of each is 1/N2. (In a rectangle we include its interior points and the points of its boundary).