This assignment uses the website www.WolframAlpha.com as a tool to help you solve some problems in multivariable calculus. You should be familiar with the site from the previous project.

Note: You do not need to sign up for Wolfram "Pro" or create an account to use the site for this assignment. If you are prompted to create an account, look for the link to continue using the free version.

Solve the following problems:

Plotting surfaces. In the last project, you graphed and named several quadric surfaces. In this problem, you will identify any saddle points and extrema for these functions.

1. For each of the following functions or equations, *Plot the surface. *Determine if it has a maximum, minimum, or a saddle point. *Give the approximate xy-coordinates of the extrema or saddle point. 1. 2. 3. 4. 5. 6.

Note that these are the same equations graphed in the previous project. 2. Optimization. Page 462, problem 43 (in the e-book). The answer is in the back of the (online) book, but you will need to set up the correct function and enter it into WolframAlpha, as you did for the surfaces in problem 1. I want to see the correct function, the plot of the surface, along with the correct dimensions and maximum volume.

Find the dimensions of a rectangular package of maximum volume that may be sent by a shipping company assuming that the sum of the length and girth