1. Chapter 4 The Exponential and Natural Logarithm Functions

2. § 4.1 Exponential Functions

3. Exponential Function DefinitionExample Exponential Function: A function whose exponent is the independent variable

4. Properties of Exponential Functions

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

6. Solving Exponential EquationsEXAMPLE Solve the following equation for x.

7. § 4.2 The Exponential Function e x

8. The Number e DefinitionExample e: An irrational number, approximately equal to 2.718281828, such that the function f (x) = b x has a slope of 1, at x = 0, when b = e

9. The Derivatives of a x and e x (a x )’ = a x Lna Example

10. § 4.3 Differentiation of Exponential Functions

11. Chain Rule for e g ( x )

12. EXAMPLE Differentiate.

13. § 4.4 The Natural Logarithm Function

14. The Natural Logarithm of x DefinitionExample Natural logarithm of x: Given the graph of y = e x, the reflection of that graph about the line y = x, denoted y = ln x

15. Properties of the Natural Logarithm

16. § 4.5 The Derivative of ln x

17. Derivative Rules for Natural Logarithms

18. Differentiating Logarithmic ExpressionsEXAMPLE Differentiate.

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