5.4: Exponential Functions: Differentiation and Integration Mt. Rushmore, South Dakota 5.4: Exponential Functions: Differentiation and Integration Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007
Objectives Develop properties of the natural exponential function. Differentiate natural exponential functions. Integrate natural exponential functions.
The inverse of is
Solve
Solve
Operations with Exponential Functions:
1. The domain of is 2. is continuous, increasing and one-to-one. 3. is concave upward on its entire domain. 4.
Find the derivative of
is its own derivative! If we incorporate the chain rule:
Find the derivative of Find the derivative of
Find the relative extrema of
Normal Probability Density Function: (Bell-shaped curve) General Form of Normal Probability Density Function:
Integrals of Exponential Functions:
Homework 5.4 (page 347) #5-17 odd 37-59 odd 87-105 odd 111