Management Calculus Fall 2020 Exam 3 Read the instructions carefully: Show all your work for partial credit

Management Calculus Fall 2020 Exam 3

Read the instructions carefully:

Show all your work for partial credit. 

Answers with no supporting work will be given no credit. 

Be sure to simplify your final answers. Use positive exponents. 

Label answers with the correct units where appropriate. 

1. Given ????(????) = 2????³ + 3????² − 36???? + 1

1. (8 pts) Find the (x,y) coordinates of the critical point(s). 
2. (6 pts) Determine the open intervals where the function is increasing or decreasing. (use interval notation) Show test points used. 
3. (4 pts) Identify the (x,y) coordinates of the relative extrema. 
4. (8 pts) Determine the open intervals where the function is concave up and concave down. (use interval notation) Show test points used. 
5. (2 pts) Find (x, y) coordinates of point(s) of inflection. 

2.  Given

.    

A. (8 pts) Find the horizontal asymptote(s) for the function.  (Use limit for full credit.) B. (8 pts) Find the vertical asymptote(s) for the function

3. (14 pts) Find the absolute maximum and absolute minimum (x- and y- coordinates) of the function ????(????) = 4 − ????³   on the interval [-2,1].  Please use the x- y- table to organize your work.

4. A carpenter is building a shed with a rectangular base.  The fixed perimeter of the base is 54 feet.  What dimensions will maximize the area of the base of the shed? A.  (2 pts) What is the objective equation?

2. (2 pts) What is the constraint equation?
3. (8 pts) Find the dimensions of the base of the shed that will maximize the total area of the base.  Label with the correct units.

5.  Given the cost function, (????) = 0.01????² + 2.7???? + 75  , where x is the number of units. A.  (6pts) Find the actual change in cost as x changes from 100 to 120.

2. (6 pts) Estimate the change using the differential dC
3. (2 pts) How do the values in parts A and B compare?

6.  The demand for a product is ???? = ????(????) = 500 − 2???? where x is the price.   A.  (6 pts) Find the elasticity of demand, E(x).

2. (4 pts) Is demand elastic or inelastic when x=$175
3. (6 pts) Find the price x when revenue is a maximum.