Introductory calculus : : maxima, minima, and special functions / / Tunc Geveci.
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Place / Publishing House: | New York, [New York] (222 East 46th Street, New York, NY 10017) : : Momentum Press,, 2015. |
Year of Publication: | 2015 |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (216 pages) :; illustrations. |
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Table of Contents:
- 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.