11x1 t10 05 curve sketching (2011)
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Curve Sketching
Curve Sketching Look for;
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
Look for;
Curve Sketching 0,0,
1 e.g.ity discontinu of points yx
xy
Look for;
xyxx
xy ,0,1
e.g. asymptotes
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
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
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
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
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
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
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
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
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
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
596 curve Sketch the e.g. 23 xxxy
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
596 curve Sketch the e.g. 23 xxxy
9123 2 xxdx
dy
1262
2
xdx
yd
63
3
dx
yd
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
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
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
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
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
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 ,
06
1236,3when 2
2
dx
ydx
06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
06
1236,3when 2
2
dx
ydx
point turningminimum a is 53 ,
0 occur when inflection of points Possible2
2
dx
yd
0126 .. xei
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
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
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 ,
x
y
x
y
11 ,
x
y
11 ,
53 ,
5
x
y
11 ,
53 ,
32 ,
x
y
11 ,
53 ,
32 ,
5
x
y
11 ,
596 23 xxxy
53 ,
32 ,
5
x
y
11 ,
596 23 xxxy
53 ,
32 ,
5
Exercise 10F;
1bdf, 2, 4b,
5ace etc, 6bd
Exercise 10G
1, 2ace, 4b, 5c
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