MAT 1235 Calculus II Section 6.1 Inverse Functions

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Presentation transcript:

MAT 1235 Calculus II Section 6.1 Inverse Functions

Next Week Scheduling Changes I will be helping with recruiting off campus next Tuesday and Thursday. Tuesday: no class Thursday: Lab 01

Homework and … WebAssign HW 6.1 Quiz: 5.3, 6.1 First Exam: Monday Bring your tutoring record tomorrow. Please, Please study for the exam! Please read the quiz solutions Please read the grader’s comment

Preview

Part I: Review of the Inverse Functions Quick review (Read the text carefully if you do not remember the details) Part II: The relation between the derivatives of a function and its inverse function

The Quest

Existence of Inverse Functions Not all functions have corresponding inverse functions

Existence of Inverse Functions

Not all functions have corresponding inverse functions In order for an inverse function to exist, this situation cannot happen: Two distinct points have the same function value

Properties

Derivatives of Inverse Functions Let. How to find ?

Derivatives of Inverse Functions

Remarks The formula can be written equivalently as which we are going to use in later sections ( and it is easy to remember due to the wonderful design of the notations )

Remarks

Example 1

Example 1: Step 1

Example 1: Step 2

Example 1: Step 3

Expectations

The steps are designed to conform with standard presentation, and minimize the chance of making mistakes. In the exam, I will look for the expected steps.