Calculus homework?
BUS 305
Spring 2017
Exam 3, 35 points
Instructions: this part of your exam is worth 35 points, and the other 35 points can be found by clicking the Exam 3 link. You have several options for submitting your work on this part of the exam.
You can type your answers into the exam file, save it using your name as part of the file name, and return the file to me as an email attachment.
You can print the questions, do your work on paper, photograph or scan each page of your handwritten work, and return those images to me as an email attachment. I recommend that you write your name on each page.
For each question, show your work in enough detail that I can determine your steps. Partial credit will be given where possible, but you must show your work. You may use course resources for this test, but you must not collaborate with any other person. Each question is worth 5 points.
1. Simplify the following expression as much as possible.
2. Find and clearly report the values of x that solve this equation.
3. Solve this inequality for x.
4. The derivative of a function is 
Compare how the original function behaves at x = 2 and at x = 3. Be complete, and support your answer with numbers.
5. Find the derivative of this function:
6. The cost accountants for a manufacturer of robotic machine equipment has determined the following information about one of the company’s products.
The product’s selling price is $3600
The cost to make x units of the product is given by the formula
a. Write the simplified expression for the profit from making and selling x units of the product.
b. Determine, using the first and second derivative and showing your work, the number of units to make and sell that will maximize profit. NOTE: demand for this product will never exceed 75 units.
7. In BUS 205, one of the probability distributions you studied was the continuous uniform distribution. This distribution is described by the density function
for values of x between a and b
for values of x smaller than a (the lower end) and larger than b (the upper end)
For this problem, assume that the time it takes to complete one of the assembly stages of the product in problem 6 is uniformly distributed between 600 and 1500 seconds.
Recall that the definite integral can be used to determine the “area under a curve.” In this case, the function shown above plots as a straight line, but we can still use the integral to find probability.
Show the steps to use the definite integral of the uniform distribution function to find the probability that the time to complete the assembly will be between 1000 and 1200 seconds.
