Wetzel                                                                                                                                                                                                              Summer 2006

Math 140

Test #3

                                                                                                                                                                                        Name: ______________________

Please read each problem carefully and check your work.

1.)  Given the function,

A.)    Construct a First Derivative Sign Diagram below.

__________________________________________

            B.)  Construct a Second Derivative Sign Diagram below.

__________________________________________

            C.)  Find the intercepts.

                        x – intercept: ___________                  y – intercept: ____________

            D.)  Sketch the graph.

2.)  Given the function, 

A.)     List all of the Critical Numbers .  _____________________

B.)     Write the equation for  any and all of the following asymptotes.  If the function does not have one, state   “Does Not Exist.”

Vertical: ___________

Horizontal:___________

Slant or Oblique: ___________

3.)    Find the following limits.

A.)                                     B.) 

4.)  Find any and all absolute extreme values for the function,

            G(x) =  on [0,5]

5.)  A Norman window is constructed by adjoining a semi-circle to the top of an ordinary rectangular window.  Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet.  [10 pts]

6.)  An open top box is to be made from a 2 ft. by 3 ft. piece of cardboard by cutting equal squares from the corners and turning up the sides.  Find the exact dimensions of the box that maximizes the volume.  Indicate the units for your solution.  [10 pts]