Exercise Three: Solution (Algebraic)

Problem:
Find the value of x for which A is a maximum. Also determine that maximum value.


Solution:
Recognize that A is a quadratic function of x and that the graph of the relationship
between x and A is a parabola.  The maximum will therefore occur at the vertex. 
The x coordinate of the vertex is given by

Then

Answer:
A has a maximum value of 16 when x is 4.

Solution (calculus)

Exercise Two Exercise Four