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