Download presentation

Presentation is loading. Please wait.

Published byDorothy Tong Modified over 2 years ago

1
MAT 1221 Survey of Calculus Section B.1, B.2 Implicit Differentiation, Related Rates http://myhome.spu.edu/lauw

2
Expectations Use equal signs Simplify answers Double check the algebra

3
HW WebAssign HW B.1, B.2 Additional HW listed at the end of the handout (need to finish, but no need to turn in) Need to do your homework soon. Do not wait until tomorrow afternoon.

4
Exam 1 Bring your Tutoring Bonus paper to class on Thursday.

5
Exam 1 You should have already started reviewing for Exam 1 Proficiency: You need to know how to do your HW problem on your own You need to understand how to solve problems Memorizing the solutions of all the problems is not a good idea

6
Preview Extended Power Rule Revisit The needs for new differentiation technique – Implicit Differentiation The needs to know the relation between two rates – Related Rates

7
Extended Power Rule

11
If y is a function in x, then

12
Extended Power Rule

13
Example 0

14
The Needs for Implicit Differentiation…

15
Example 1 Find the slopes of the tangent line on the graph i.e. find x y

16
Example 1: Method I x y

17
x y

18
Make y as the subject of the equation: x y

19
Example 1: Method I Suppose the point is on the upper half circle x y

20
Example 1: Method I Suppose the point is on the lower half circle x y

21
Example 1: Method I Two disadvantages of Method I: 1. ??? 2. ???

22
Example 1: Method II Implicit Differentiation: Differentiate both sides of the equation.

23
Expectation You are required to show the implicit differentiation step

24
Notations

25
Example 2 Find the slope of the tangent line at

26
Notations

27
Correct or Incorrect because

28
B.2. Related Rates

29
Related Rates

31
Example 3 Consider a “growing” circle.

32
Example 3 Both the radius and the area are increasing.

33
Example 3 What is the relation between and ?

34
Example 1 GO NUTS!

35
Example 1 GO NUTS!

36
Example 3 A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at 3 feet per second, how fast is the area changing when the radius is 5 feet?

37
Step 1 Draw a diagram A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at 3 feet per second, how fast is the area changing when the radius is 5 feet?

38
Step 2: Define the variables A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at 3 feet per second, how fast is the area changing when the radius is 5 feet?

39
Step 3: Write down all the information in terms of the variables defined A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at 3 feet per second, how fast is the area changing when the radius is 5 feet?

40
Step 4: Set up a relation between the variables

41
Step 5: Use differentiation to find the related rate Formal Answer When the radius is 5 feet, the area is changing at a rate of …

42
Steps for Word Problems 1. Draw a diagram 2. Define the variables 3. Write down all the information in terms of the variables defined 4. Set up a relation between the variables 5. Use differentiation to find the related rate. Formally answer the question.

43
Remark on Classwork #2 To save time, problem number 2 does not required all the steps.

44
Expectations

Similar presentations

Presentation is loading. Please wait....

OK

MAT 1234 Calculus I Section 2.8 Part II Related Rates II

MAT 1234 Calculus I Section 2.8 Part II Related Rates II

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power line communication adapters Viewer ppt online Ppt on life processes for class 10 cbse Ppt on self development skills Ppt on network switching tutorial Ppt on condition based maintenance Ppt on bond length of hcl Ppt on power grid failure video Ppt on nitrogen cycle and nitrogen fixation definition Ppt on organic chemistry-some basic principles and techniques