11 x1 t10 04 maximum & minimum problems (2012)
-
Upload
nigel-simmons -
Category
Education
-
view
697 -
download
0
Transcript of 11 x1 t10 04 maximum & minimum problems (2012)
![Page 1: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/1.jpg)
Maximum/Minimum Problems
![Page 2: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/2.jpg)
Maximum/Minimum ProblemsMaximum/minimum problems involve finding the vertex of a quadratic
![Page 3: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/3.jpg)
Maximum/Minimum ProblemsMaximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
![Page 4: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/4.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
![Page 5: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/5.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
![Page 6: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/6.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
![Page 7: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/7.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
![Page 8: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/8.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
![Page 9: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/9.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
21 113 46 12
x
![Page 10: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/10.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
11maximum value is 412
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
21 113 46 12
x
![Page 11: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/11.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
11maximum value is 412
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
21 113 46 12
x
OR 21 4 3 559
![Page 12: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/12.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
11maximum value is 412
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
21 113 46 12
x
OR 21 4 3 559
maximum value4a
![Page 13: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/13.jpg)
Maximum/Minimum Problems
2e.g. ( ) Find the maximum value of 3 5i y x x
23 5y x x 2 13 5
3x x
21 13 5
6 12x
11maximum value is 412
Maximum/minimum problems involve finding the vertex of a quadraticRead the question carefully to see if it is the x value or the y value you are required to find.
(Need to find the y value of the vertex)
21 113 46 12
x
OR 21 4 3 559
maximum value4a
5912
11412
![Page 14: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/14.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
![Page 15: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/15.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
![Page 16: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/16.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
![Page 17: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/17.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s
![Page 18: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/18.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
![Page 19: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/19.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
![Page 20: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/20.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
232A s s
![Page 21: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/21.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
232A s s
2 32s s
![Page 22: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/22.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
232A s s
2 32s s
216 256s
![Page 23: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/23.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
232A s s
2 32s s
216 256s
dimensions for a maximum area are 16cm 16cm
![Page 24: 11 x1 t10 04 maximum & minimum problems (2012)](https://reader033.fdocuments.net/reader033/viewer/2022060200/5597e0591a28ab5e388b4880/html5/thumbnails/24.jpg)
(ii) A rectangle has perimeter of 64 cm. What dimensions would the rectangle have for maximum area?
s
32 s 32A s s
We want the dimensions, so it is the x value of the vertex we need to find.
232A s s
2 32s s
216 256s
dimensions for a maximum area are 16cm 16cm
Exercise 8E; 1a iv, 2a iii, then multiples of 3