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Chapter 4 The Exponential and Natural Logarithm Functions

Chapter 4 The Exponential and Natural Logarithm Functions. § 4.1. Exponential Functions. Exponential Function. Properties of Exponential Functions. Graphs of Exponential Functions.

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Chapter 4 The Exponential and Natural Logarithm Functions

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  1. Chapter 4The Exponential and Natural Logarithm Functions

  2. §4.1 Exponential Functions

  3. Exponential Function

  4. Properties of Exponential Functions

  5. Graphs of Exponential Functions Notice that, no matter what b is (except 1), the graph of y = bx has a y-intercept of 1. Also, if 0 < b < 1, the function is decreasing. If b > 1, then the function is increasing.

  6. Solving Exponential Equations EXAMPLE Solve the following equation for x.

  7. §4.2 The Exponential Function ex

  8. The Number e

  9. The Derivatives of ax and ex (ax)’ = axLna Example

  10. §4.3 Differentiation of Exponential Functions

  11. Chain Rule for eg(x)

  12. Chain Rule for eg(x) EXAMPLE Differentiate.

  13. §4.4 The Natural Logarithm Function

  14. The Natural Logarithm of x

  15. Properties of the Natural Logarithm

  16. §4.5 The Derivative of ln x

  17. Derivative Rules for Natural Logarithms

  18. Differentiating Logarithmic Expressions EXAMPLE Differentiate.

  19. Differentiating Logarithmic Expressions EXAMPLE The function has a relative extreme point for x > 0. Find the coordinates of the point. Is it a relative maximum point?

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