Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By...
Transcript of Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By...
![Page 1: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/1.jpg)
By Gökhan Bilhan 1
Calculus 3
(Week 5)-Max-Min
Note that, if there is a greatest local maximum point, it is calledAbsolute Maximum Point.
On the other hand, if there is a smallest local minimum point, it iscalled Absolute Minimum Point.
Definition.(Critical Point) A point (a, b) is called a critical point of f , if
fx(a, b) = 0 and fy(a, b) = 0
OR
If one of these partial derivatives does not exist.
![Page 2: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/2.jpg)
By Gökhan Bilhan 2
Example. Let’s look at local max-min of the following function,
f(x, y) = x2 + y2 − 2x− 6y + 14
Remark. Sometimes, local max, local min values called ’Extreme Values’.
Example. Find the extreme values of the function f(x, y) = y2 − x2.
![Page 3: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/3.jpg)
By Gökhan Bilhan 3
![Page 4: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/4.jpg)
By Gökhan Bilhan 4
..
![Page 5: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/5.jpg)
By Gökhan Bilhan 5
![Page 6: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/6.jpg)
By Gökhan Bilhan 6
..
![Page 7: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/7.jpg)
By Gökhan Bilhan 7
Exercises.
![Page 8: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/8.jpg)
By Gökhan Bilhan 8
PART 2
![Page 9: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/9.jpg)
By Gökhan Bilhan 9
Example. Find the absolute max. and min. values of f on the set D, if
![Page 10: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/10.jpg)
By Gökhan Bilhan 10
Exercises.
![Page 11: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/11.jpg)
By Gökhan Bilhan 11
Exercises of the Week
1-) Find the local max-min and saddle points (if there is any) of the following.
![Page 12: Calculus 3kisi.deu.edu.tr/gokhan.bilhan/2016 2017 guz/CalculusIII-3-2-Max-Min-Week5.pdf · By Gökhan Bilhan 1 Calculus 3 (Week 5)-Max-Min Note that, if there is a greatest local](https://reader033.fdocuments.us/reader033/viewer/2022042212/5eb61f1e59c6e21a6925f9e5/html5/thumbnails/12.jpg)
By Gökhan Bilhan 12
2-) Find the absolute max-min points of the following.