Applications of Derivatives
Comprehensive calculus applications using derivatives to solve rates, optimization, graphing, asymptotes, and approximation problems.
Related rates, linear approximations, extrema and optimization, mean value theorem, curve shape, asymptotes, L'Hôpital, Newton, antiderivatives
Setting up Related-Rates Problems
Examples of the Process
Linear Approximation of a Function at a Point
Differentials
Calculating the Amount of Error
Absolute Extrema
Local Extrema and Critical Points
Locating Absolute Extrema
Rolle’s Theorem
The Mean Value Theorem and Its Meaning
Corollaries of the Mean Value Theorem
The First Derivative Test
Concavity and Points of Inflection
The Second Derivative Test
Limits at Infinity
End Behavior
Guidelines for Drawing the Graph of a Function
Solving Optimization Problems over a Closed, Bounded Interval
Solving Optimization Problems when the Interval Is Not Closed or Is Unbounded
Applying L’Hôpital’s Rule
Other Indeterminate Forms
Growth Rates of Functions
Describing Newton’s Method
Failures of Newton’s Method
Other Iterative Processes
The Reverse of Differentiation
Indefinite Integrals
Initial-Value Problems