1. MAT 1235 Calculus II Section 6.1 Inverse Functions http://myhome.spu.edu/lauw

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

3. 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

4. Preview

5. 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

6. The Quest

9. Existence of Inverse Functions Not all functions have corresponding inverse functions

10. Existence of Inverse Functions

11. 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

12. Properties

13. Derivatives of Inverse Functions Let. How to find ?

14. Derivatives of Inverse Functions

18. 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 )

19. Remarks

20. Example 1

21. Example 1: Step 1

22. Example 1: Step 2

23. Example 1: Step 3

24. Expectations

25. 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.