Download - 11X1 T10 01 first derivative (2011)
Geometrical Applications
of Differentiation The First Derivative
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
decreasing is curve the,0 If xf
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
curve sketch the Hence
nature. their determine and
points stationary theof all find ,3 curve For the e.g. 32 xxy
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
curve sketch the Hence
nature. their determine and
points stationary theof all find ,3 curve For the e.g. 32 xxy
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
236 xxdx
dy
0 occur when points Stationary dx
dy
0 occur when points Stationary dx
dy
036 .. 2 xxei
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1)
(-9)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1)
(3)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3) (-9)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3) (-9)
point turningmaximum a is 2,4
x
y
x
y
x
y
2,4
x
y
2,4
323 xxy
Exercise 10A; 1, 2ace, 4, 5, 6ac, 7, 8, 9ace etc,
11, 12, 13, 15ace, 16, 17
Exercise 10B; 1ad, 2ac, 3ac, 5, 6, 7ac, 8, 10, 12
