Derivatives - Theory

• Introduction: definition, basic properties, total differential.
• Mean value theorem and related topics (l'Hospital's rule, derivative and monotonicity/concavity).
• Graphing functions including monotonicity, concavity and asymptotes; for practical approach see Methods Survey.
• Applications: tangent line, global extrema and optimization, Taylor polynomial, approximation; for practical approach see Methods Survey.
• Implicit and parametric functions (derivative, sketching); for practical approach see Methods Survey.