5.4: Exponential Functions: Differentiation and Integration

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Presentation transcript:

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 358) #1 – 5 odd 11 – 15 odd 39 – 61 odd