Related Rate Questions

Related Rate Questions  Related Rate questions are an application of derivative. If two or more quantities help model the same situation, then their derivatives are related and may be used to examine their rates of change. these are called related rate problems. They appear on the AP Calculus exams usually as part of a free-response or…

Type 7 Questions: Miscellaneous

Any topic in the Course and Exam Description may be the subject of a free-response or multiple-choice question. There are topics that are not asked often enough to be classified as a type of their own. The two topics listed here have been the subject of full free-response questions or major parts of them. Other…

Other Derivative Applications

Some final applications of derivatives L’Hospital’s Rule  Locally Linear L’Hospital’s Demonstration of the proof L’Hospital Rules the Graph Good Question An AP Exam question that can be used to delve deeper into L’Hospital’s Rule (2008 AB 6) Related Rate problems Related Rates Problems 1   Related Rate Problems II Good Question 9  Baseball and Related Rates Painting a…

Other Topics (Type 7)

Any topic in the Course and Exam Description may be the subject of a free-response question. The two topics listed here have been the subject of full free-response questions or major parts of them. Implicitly defined relations and implicit differentiation These questions may ask students to find the first or second derivative of an implicitly…

Good Question 9

This is a good question that leads to other good questions, both mathematical and philosophical. A few days ago this question was posted on a private Facebook page for AP Calculus Readers. The problem and illustration were photographed from an un-cited textbook. Player 1 runs to first base [from home plate] at a speed of…

Painting a Point

Accumulation 7: An application (of paint) Suppose you started with a point, the origin to be specific, and painted it. You put on layers and layers of paint until your point grows to a sphere with radius r. Let’s stop and admire your work part way through the job; at this point the radius is…