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Calculus Series - Concepts and Formulas
Applications of Differentiation 2 (CLS-CF3)

This sheet provides a comprehensive review of all of the most important topics, concepts and formulas covered in differentiation applications. Each concept is explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas sheet answers questions about how to use the concepts - how to actually solve problems with them, it doesn't just list facts and formulas. There is even an example, or two, for each concept, to help you to nail down the central ideas.

Topics Covered:

• General guidelines for solving maxima and minima problems
• Tangent line approximations to the graph of a function
• Differential approximations to the graph of a function
• Proportional and percentage errors
• Newton's method of approximating zeros of a function
• How to use Newton's method to estimate the point(s) of intersection of two curves
• Conditions under which Newton's method will fail
• Inverse functions
• Derivatives of inverse functions
• The natural logarithm function, exp(x) and derivatives
• Logarithmic differentiation
• Exponential growth and decay
• Basic differential equations
• Indeterminate forms
• L'Hôpital's rule
• Hyperbolic functions
• Derivatives of hyperbolic functions

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