In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect. Research has shown that nonroutine problems in algebra may alter students' impressions of mathematics and allow for a keener sense of understanding and more productive lines of thinking. Perhaps the greatest benefit to teachers is seeing the application of important mathematical ideas outside the narrow context in which they are often introduced. An open-ended calculus problem is presented that spurs novelties in student thinking and shows the benefits of timely teacher intervention.