This problem is similar to Probem 6 on the Final Exam Study Guide. In that problem and the one below, you are given a derivative and asked to undo the derivative with an antiderivative.
Problem 7 deal with approximating area under a function using rectangles. This information is covered in Section 13.2.
In this problem you need to take a derivative in the form of marginal cost and undo the derivative to get the cost function. This is covered in Question 4 of Section13.1.
This is a basic antiderivative problem from Section 13.1. This problem requires you to use the Power Rule for Antiderivatives.
This problem asks you to find a point of diminishing returns. This is simply a business term for an inflection point. This means you need to find the second derivative and set it equal to zero. To make sure the second derivative changes sign (that is what happens at a point of inflection), you need to check the sign of the second derivative and see if it really does change.
This content is covered in Question 4 of Section 12.2.
The first problem on the midterm is a problem where you need to find the absolute maximum of a function. Since the function is defined on a closed interval, the absolute maximum or minimum occurs at the endpoints of the interval or at any critical points.
The final exam is less than a month away so it is time to start studying for it. If you are in the face to face class, you will take the final exam in class on Wednesday, December 7.
For online students, the Final Exam must be taken on either Wednesday, December 7 or Thursday, December 8. I will have the exam available at the same testing center you used for the midterm. If you need to change locations, contact me before November 18 so that I can contact the testing center.
Below is the study guide for the final exam.
- Final Exam Study Guide (PDF)
At this point, we have not covered every single question on the final exam. However, you should be able to do Problems 1, 2, 3, 4, 6, and 7.
Over the next few weeks I will post the solutions to these problems. You can search for them on the blog posts, but is probably easier to click on Final Exam Study Guide in the Categories to the left.