Maxima and Minima

01 - 04 Number Problems in Maxima and Minima

Problem 1
What number exceeds its square by the maximum amount?

Solution 1


Application of Maxima and Minima

As an example, the area of a rectangular lot, expressed in terms of its length and width, may also be expressed in terms of the cost of fencing. Thus the area can be expressed as A = f(x). The common task here is to find the value of x that will give a maximum value of A. To find this value, we set dA/dx = 0.

Maxima and Minima | Applications

Graph of the Function y = f(x)
The graph of a function y = f(x) may be plotted using Differential Calculus. Consider the graph shown below.



As x increases, the curve rises if the slope is positive, as of arc AB; it falls if the slope is negative, as of arc BC.


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