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Tangents, Normals and Turning Points
Q1)
The function (blue) is
y = – x
3
+ 6 x
2
– 3 x + 4
The green line is the tangent at
x = 0
and the red line is the normal at
x = 2
.
Find the point at which these lines meet.
x =
y =
Give your answer to 2 decimal places.
Q2)
The function (blue) is
y = 2 x
3
+ 9 x
2
+ 2 x
–
6
Find the location of the two turning points:
x
1
=
x
2
=
y
1
=
y
2
=
The green line is the tangent at
x = - 3
and the red line is the normal at
x = - 2
.
Find the point at which these lines meet.
x =
y =
Give your answer to 2 decimal places.
Q3)
The function (blue) is
y = x + (1/x) + 2
Find the location of the two turning points:
x
1
=
x
2
=
y
1
=
y
2
=
The green line is the tangent at
x = 0.5
and the red line is the normal at
x = - 0.5
.
Find the point at which these lines meet.
x =
y =
Give your answer to 2 decimal places.
Q4)
The function (blue) is
y = 2 x + ( 8 / x ) + 10
Find the location of the two turning points:
x
1
=
x
2
=
y
1
=
y
2
=
The green line is the tangent at
x = 3
and the red line is the normal at
x = - 4
.
Find the point at which these lines meet.
x =
y =
Give your answer to 2 decimal places.
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