1. Exponential functions: differentiation & integration (5.4) March 1st, 2013

2. I. the natural exponential function DEF. OF THE NATURAL EXPONENTIAL FUNTION: The inverse of is. THus, if and only if. It follows that and.

3. THM. 5.10: OPERATIONS WITH EXPONENTIAL FUNCTIONS: Let and be any real numbers. 1. 2.

4. PROPERTIES OF THE NATURAL EXPONENTIAL FUNCTION: 1. the domain of is and the range is 2. is continuous, increasing, and one-to-one 3. is concave upward 4. and

5. II. derivatives of exponential functions THM. 5.11: DERIVATIVE OF THE NATURAL EXPONENTIAL FUNCTION: Let u be a differentiable function of x. 1. 2.

6. EX. 1: Find the derivative of each function. a. b.

7. EX. 3: Find the extrema and points of inflection of.

8. III. integrals of exponential functions THM. 5.12: INTEGRATION RULES FOR EXPONENTIAL FUNCTIONS: Let u be a differentiable function of x. 1. 2.

9. EX. 3: Find each indefinite integral. a. b. c.

10. EX. 4: Evaluate.