Solving the Volume of an Object with Polynomial Functions
I've been stuck on a fairly difficult (well, for me at least) problem all day. It's concerning the volume in cubic feet of a CD holder:
The volume in cubic feet of a CD holder can be expressed as The following are problems relating to the info above:
or, when factored, as the product of its three dimensions, depth, height, and width. The depth is expressed as (2 - x). Assume the height is greater than the width.
a. Factor the polynomial to find linear expressions for the height and the width.I've been doing a lot of problems like this in my Algebra 2 class, and I just need a simple explanation on what to do. I know how to graph a polynomial function like this, so (b.) shouldn't be a problem.
b. Sketch a graph of the function. Find the x-intercepts. Explain what the x-intercepts represent geometrically.
c. Describe a realistic domain for the function V(x) and explain why you consider it to be realistic.
d. Find the maximum volume of the CD holder.