5.1 (Part II): The Natural Logarithmic Function and Differentiation

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Presentation transcript:

5.1 (Part II): The Natural Logarithmic Function and Differentiation Mt. Rushmore, South Dakota Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007

Objectives Develop and use properties of the natural logarithmic function. Understand the definition of the number e. Find derivatives of functions involving the natural logarithmic function.

Sometimes you can use logarithms to help differentiate non-logarithmic functions.

Take ln of both sides of the equation. Differentiate of both sides of the equation.

You can ignore the absolute value signs! Proof:

Find the relative extreme of int c f '(c) (-∞,-1) -2 - (-1,∞) +

Homework 5.1 (page 331) # 65 – 77 odd, 83, 87 – 93 odd, 101-105 odd