(University of California, Los Angeles)
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Ch. 4: Applications of the Derivative
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Conceptual Insights encourage students to develop a conceptual understanding of calculus by explaining important ideas clearly but informally.
Graphical Insights enhance students’ visual understanding by making the crucial connections between graphical properties and the underlying concepts.
Reminders are margin notes that link the current discussion to important concepts introduced earlier in the text to give students a quick review and make connections with related ideas.
Caution notes warn students of common pitfalls they may encounter in understanding the material. Examples work through problems to instruct students on concepts. They contain full, stepped-out solutions for each part.
Historical Perspectives are brief vignettes that place key discoveries and conceptual advances in their historical context. They give students a glimpse into some of the accomplishments of great mathematicians and an appreciation for their significance.
Assumptions Matter uses short explanations and well-chosen counterexamples to help students appreciate why hypotheses are needed in theorems.
Section Summaries summarize a section’s key points in a concise and useful way and emphasize for students what is most important in each section.
Section Exercise Sets offer a comprehensive set of exercises closely coordinated with the text. These exercises vary in difficulty from routine, to moderate, to more challenging.
Chapter Review Exercises offer a comprehensive set of exercises closely coordinated with the chapter material to provide additional problems for self-study or assignments.
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