1. Increasing and decreasing functions and extrema -- Some terminology -- The derivative test for monotonicity and extrema -- The proof of Fermat's theorem --

2. Understanding the mean value theorem -- Rolle's theorem and the mean value theorem --

3. Determining concavity and extrema -- The second derivative and extrema -- The proof of the second derivative test for local extrema --

4. Drawing the graph of a function --

5. Using maxima and minima in real applications -- Optimization -- Applications to economics --

6. The importance of inverse functions -- Inverse trigonometric functions --

7. Using the derivative of an inverse function -- The general expression -- The derivatives of inverse trigonometric functions -- The proof of theorem 1 (optional) --

8. Applying the natural exponential function and the natural logarithm -- The natural logarithm --

9. Exponential functions with arbitrary bases -- Logarithmic functions with arbitrary bases -- Arbitrary powers of x --

10. Orders of magnitude in exponential functions -- Logarithmic growth -- The natural exponential function as a limit of polynomials --

11. Using exponential functions in growth and decay rates -- The solution of the differential equation y = ky -- Compound interest --

12. Introduction to hyperbolic and inverse -- Hyperbolic functions -- Inverse hyperbolic functions --

13. Using L'Hopital's rule for indeterminate forms -- The indeterminate form 0/0 -- The indeterminate form [infinity] / [infinity] -- The indeterminate form 0 / [infinity] -- The indeterminate forms 1[infinity], [infinity]0 and 00 -- The indeterminate form [infinity] - [infinity] --

Index.