Optimization
Introduction
Optimization in calculus is determining the appropriate equation to describe a situation. You then take the derivative of that equation to find a turning point. This will usually be a minimum or maximum. The problems that require you to find the maximum height of a rocket are basic optimization problems.
For example,
Of all rectangles with perimeter 24cm, which dimensions yield the largest area?
A = LW Let x = length and (12 – x) = width.
1.1 A field is already bounded on one side by a pre-existing fence. Three adjacent pens are to be enclosed by 800 feet of fence. Find the dimensions of the pens of maximum area (The pens are equal in area).
1.2 
a) 
b) Use the TI to find the minimum length (P + Q) and the location of E at this point.
Graph the function
Look at the graph of the equation and use the minimum tool on the calculator to find a value of x. The TI will give you an answer of 2. The location is 2 units away from C.
c) Find the minimum (P + Q).
Substitute 2 in for x to find the length of (P + Q)
d) Find the maximum (P + Q)
From looking at the graph we can tell that either point x = 0 or 6 are relative maximums of (P + Q). To find the value that yields the highest (P + Q) use the value function of a graph on the TI, or substitute in 0 and 6 and solve.
