Applications

There are many applications of polynomials. One of the most important is volume of a rectangular prism. Recall that the formula to determine volume of a rectangular prism is: V = lwh, where l = length, w = width and h = height.

Example Find the function that models the volume of a rectangular cereal box with length (15 - x), width (12 - x) and height (x). Determine the maximum volume of the prism.

Step 1. Use substitution to write a function in factored form.

app_ex1

Step 2. To determine maximum volume, find the local maxima of the graph.

app_ex2

Step 3. Determine the maximum volume for the box.

Since the local maxima is contained within the domain of this function:

the maximum volume will be 354.47 cubic units.