11x1 t10 05 curve sketching (2011)
TRANSCRIPT
![Page 1: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/1.jpg)
Curve Sketching
![Page 2: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/2.jpg)
Curve Sketching Look for;
![Page 3: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/3.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
Look for;
![Page 4: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/4.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
Look for;
xyxx
xy ,0,1
e.g. asymptotes
![Page 5: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/5.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
Look for;
xyxx
xy ,0,1
e.g. asymptotes
![Page 6: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/6.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
xyxx
xy ,0,1
e.g. asymptotes
![Page 7: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/7.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
![Page 8: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/8.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
![Page 9: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/9.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
![Page 10: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/10.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
is; curveA
![Page 11: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/11.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
0 if increasing xf
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
is; curveA
![Page 12: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/12.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
0 if increasing xf
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
is; curveA
0 if decreasing xf
![Page 13: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/13.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
0 if increasing xf
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
is; curveA
0 if decreasing xf
0 if up concave xf
![Page 14: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/14.jpg)
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
xfy curve On the
0 occur when points stationary 1 xf
Look for;
0 if increasing xf
xyxx
xy ,0,1
e.g. asymptotes
0,0 ifpoint turningmaximum 2 xfxf
0,0 ifpoint turningminimum 3 xfxf
0concavity
in change a is thereand 0 if inflection ofpoint 4
xf
xf
is; curveA
0 if decreasing xf
0 if up concave xf
0 ifdown concave xf
![Page 15: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/15.jpg)
596 curve Sketch the e.g. 23 xxxy
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596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
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596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
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596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
63
3
dx
yd
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596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy6
3
3
dx
yd
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596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy
09123 i.e. 2 xx
63
3
dx
yd
![Page 21: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/21.jpg)
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy
09123 i.e. 2 xx
031
0342
xx
xx
63
3
dx
yd
![Page 22: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/22.jpg)
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy
09123 i.e. 2 xx
031
0342
xx
xx
3or 1 xx
63
3
dx
yd
![Page 23: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/23.jpg)
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy
09123 i.e. 2 xx
031
0342
xx
xx
3or 1 xx
63
3
dx
yd
06
1216,1when 2
2
dx
ydx
![Page 24: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/24.jpg)
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
0 occur when points Stationary dx
dy
09123 i.e. 2 xx
031
0342
xx
xx
3or 1 xx
63
3
dx
yd
06
1216,1when 2
2
dx
ydx
point turningmaximum a is 11 ,
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06
1236,3when 2
2
dx
ydx
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06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
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06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
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06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
0126 .. xei
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06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
0126 .. xei
2x
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06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
0126 .. xei
2x
06,2when 3
3
dx
ydx
![Page 31: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/31.jpg)
06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
0126 .. xei
2x
06,2when 3
3
dx
ydx
inflection ofpoint a is 32 ,
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x
y
![Page 33: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/33.jpg)
x
y
11 ,
![Page 34: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/34.jpg)
x
y
11 ,
53 ,
5
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x
y
11 ,
53 ,
32 ,
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x
y
11 ,
53 ,
32 ,
5
![Page 37: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/37.jpg)
x
y
11 ,
596 23 xxxy
53 ,
32 ,
5
![Page 38: 11X1 T10 05 curve sketching (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042516/55949f691a28ab30398b4584/html5/thumbnails/38.jpg)
x
y
11 ,
596 23 xxxy
53 ,
32 ,
5
Exercise 10F;
1bdf, 2, 4b,
5ace etc, 6bd
Exercise 10G
1, 2ace, 4b, 5c