Introductory calculus : : maxima, minima, and special functions / / Tunc Geveci.

• VerfasserIn: Geveci, Tunc.,
• Place / Publishing House: New York, [New York] (222 East 46th Street, New York, NY 10017) : : Momentum Press,, 2015.
• Year of Publication: 2015
• Language: English
• Physical Description: 1 online resource (216 pages) :; illustrations.
• Notes: Co-published with Cognella Academic Publishing.; Includes index.

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.