Assessment Standards
6.2 
Can compute the derivatives and integrals involving exponential functions. 
6.4 
Can compute the derivative and integrals involving log functions. 
Applications of Integration 5.1 Can compute the area between curves 5.2 Can compute volumes of revolution using disks 5.5 Can compute the average value of a function
We're working through the unstarred units in chapter 6.
Chapter 6  Logarithmic and Exponential Functions


Inverse Functions
· The use of multiple representations (verbal, numeric, visual, algebraic) to understand inverse functions, always returning to the central idea of reversing inputs and outputs.
· Use of implicit differentiation to find the derivative of an inverse function.

Functions relate inputs to outputs. What if we’re given the output and we need to find the input? Most functions have inverse functions, and we’ll learn how inverse functions are treated in calculus.
Inverse Functions
NonInvertible Functions

Exponential Functions and Their Derivatives
· Comparing relative magnitudes of functions, their rates of change (e.g. exponential vs. polynomial vs. logarithmic).
· Algebraic and geometric properties of exponential functions.
· Translation and reflection of exponential functions, from both symbolic and geometric perspectives.
· Derivatives of exponential functions. The definition of e.

Exponential functions are everywhere in nature, from biology, to nuclear physics. We need to understand their behavior, and how to study the rate of change of exponential functions.
Exponential Functions
The number e
The Natural Exponential Function
Calculus of General Exponentials Functions

Logarithmic Functions
· Comparing magnitudes of functions, their rates of change.
· Logarithmic functions and their properties, including their geometric properties as inverses of exponentials.
· Graphs of logarithmic functions, including asymptotic behavior.

The logarithm is the inverse of the exponential. What are logarithmic functions, and why are they useful?
Logarithmic Functions
Solving Exponential and Logarithmic Functions
Changing the Base of a Logarithmic Function

Derivatives of Logarithmic Functions
· Derivatives and integrals of logarithmic functions.

We will discover the huge importance of the derivative of logarithm functions.
Natural Logarithmic Functions and their Derivatives
Calculus of General Logarithmic Functions


Homework  Problems 

5A  [u5.1: 1, 3, 5, 9, 11, 13, 17, 19, 27, 31, 35, 37, 46][u5.2: 1, 5, 7, 9, 11, 13, 15, 25, 29, 49]  5B  [u5.3: 1, 5, 7, 9, 13, 15, 17, 21, 37, 39, 45, 47]  5C  [u5.4: 1, 3, 7, 9, 11, 13, 15, 19, 21] [u5.5: 1, 7, 9, 11, 13, 17, 19]  6A  Inverse Functions and Exponentials  [u6.1: 1, 3, 5, 9, 13, 17, 19, 21, 23, 25, 31, 35, 39, 41] [u6.2: 1, 5, 11, 15, 25, 29, 33, 37, 43, 51, 67, 69, 79, 83, 87]  6B  Logarithms and Derivatives of Logs  [u6.3: 1, 5, 7, 11, 13, 15, 21, 25, 29, 35, 37, 39, 47, 49, 57, 59, 61, 65] [u6.4: 7, 9, 15, 19, 27, 33, 35, 47, 73, 75, 81]  6C  Inverse Trig Functions  [u6.6: 1, 3, 5, 7, 13, 15, 23, 29, 31, 37, 43, 45, 59, 61, 63] 
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ĉ Nikhil Joshi, Mar 31, 2015, 2:10 PM
