A function f(x) is said to be maximum (i.e. has attained its maximum value) at a point, if the function cases to increase and begins to decrease at that point. Symbolically, it can be represented as f(a) ≥ f(a+ h), where, h is the sufficiently small increment and a is the point to which f(x) approaches.

On the other hand, a function, f(c) is said to be minimum (i.e., has attained its minimum value) at a point, if the function ceases to decrease and begins to increase at that point. Symbolically, this can be represented as f(a) ≤ f(a + h) where, *h is the sufficiently small increment and a is the point to which f(x) approaches.*

The concept of maxima and minima of a function will be made more clear from the following graphs.

From the above graph it must be noticed that the points c_{1} and C_{3} are the minimum and the points C_{2 }and C4 are the maximum points of the graph. The function f(x) has maximum values Q_{2}C_{2} and Q_{4}C_{4} when x = OQ_{2} and OQ_{4} respectively. On the other hand, the function f(x) has maximum values Q_{1}C_{1} and Q_{3}C_{3} when x = OQ_{1} and OQ_{3} respectively.