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 $dA/dx = 0$.
 

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.