Wetzel                                                                                                                                                                                                      Summer 2006

Math 130

Test #2

                                                                                                                                                                                Name: _______________________

NO GRAPHING CALCULATORS ALLOWED!!  You may use a scientific calculator if you wish.  Read each problem carefully and completely answer each question.  Good luck!

1.)  Given the function, f(x) = ,

            a.)  Construct a first derivative sign diagram.

                        _________________________________________

            b.)  Construct a second derivative sign diagram.

                        _________________________________________

c.)    Find the intercepts.

x-intercept: __________                            y-intercept: __________

            d.)  Sketch the graph.

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

            G(x) =  on [0,5]

3.)  Use implicit differentiation to find  of the following equation.

5.)  An open box is to be made from a two-foot by three-foot rectangular piece of material by cutting equal squares from the corners and turning up the sides.  Find the volume of the largest box that can be made in this manner.

6.)  When a wholesaler sold a product at $40 per unit, sales were 300 units per week.  After a price increase of $5, however, the average number of units sold dropped to 275 per week.  Assuming that the demand function in linear, what price per unit will yield a maximum total revenue?

7.)  A child throws a stone into a still millpond causing a circular ripple to spread.  If the radius of the circle increases at the constant rate of 0.5 feet per second, how fast is the area of the ripple increasing when the radius of the ripple is 30 feet? (Area of a circle is equal to  times the radius squared)