MAT 1235 Calculus II Section 6 1 Inverse

Homework and … l l l l Web. Assign HW 6. 1 Quiz: 5.

Preview l Part I: Review of the Inverse Functions • Quick review (Read the

Existence of Inverse Functions l Not all functions have corresponding inverse functions

Existence of Inverse Functions l l Not all functions have corresponding inverse functions In

Derivatives of Inverse Functions l Let . How to find ?

Remarks The formula can be written equivalently as which we are going to use

Expectations l The steps are designed to l In the exam, I will look

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MAT 1235 Calculus II Section 6. 1 Inverse Functions http: //myhome. spu. edu/lauw

Homework and … l l l l Web. Assign HW 6. 1 Quiz: 5. 3, 6. 1 First Exam: Wednesday 1: 45 -2: 50 Bring your tutoring record Monday. Please, Please study for the exam! Please read the quiz solutions Please read the grader’s comment

Preview l

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

The Quest l

The Quest

Existence of Inverse Functions l Not all functions have corresponding inverse functions

Existence of Inverse Functions

Existence of Inverse Functions l l 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 l

Derivatives of Inverse Functions l 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)

Example 1

Example 1: Step 1 l

Example 1: Step 2

Example 1: Step 3

Expectations l

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