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 $dA/dx = 0$.

Steps in Solving Maxima and Minima Problems

  1. Identify the constant, say cost of fencing.
  2. Identify the variable to be maximized or minimized, say area $A$.
  3. Express this variable in terms of the other relevant variable(s), say $A = f(x, ~ y)$.
  4. If the function shall consist of more than one variable, expressed it in terms of one variable (if possible and practical) using the conditions in the problem, say $A = f(x)$.
  5. Differentiate and equate to zero, $dA/dx = 0$.