lecture20

# lecture20 - And through investigation we recognize that 81...

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Math 121 Lecture 20 The Product and Quotient Rules

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! Exponential Functions ! The Exponential Function e x ! Differentiation of Exponential Functions ! The Natural Logarithm Function ! The Derivative ln x ! Properties of the Natural Logarithm Function § 4.1 Exponential Functions

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! Exponential Functions ! Properties of Exponential Functions ! Simplifying Exponential Expressions ! Graphs of Exponential Functions ! Solving Exponential Equations Definition Example Exponential Function : A function whose exponent is the independent variable y = " 2 ( ) x , y = 5 x
Write each function in the form 2 kx or 3 kx , for a suitable constant k . (a) We notice that 81 is divisible by 3.

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Unformatted text preview: And through investigation we recognize that 81 = 3 4 . Therefore, we get (b) We first simplify the denominator and then combine the numerator via the base of the exponents, 2. Therefore, we get Notice that, no matter what b is (except 1), the graph of y = b x has a y-intercept of 1. Also, if 0 < b < 1, the function is decreasing. If b > 1, then the function is increasing. Solve the following equation for x . This is the given equation. Factor. Simplify. Since 5 x and 6 – 3 x are being multiplied , set each factor equal to zero. 5 x " x = 2 5 x ! 0....
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## This document was uploaded on 09/30/2010.

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lecture20 - And through investigation we recognize that 81...

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