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Bài tập CALCULUS 38
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Created by T. Madas
Question 142
(***+)
The curve C has equation
y = x3 − 3 x 2 + 3 x + 5 .
Show that C has only one stationary point and determine its nature.
MP1-B , point of inflection at (1,6 )
Question 143
(***+)
Prove by showing all the parts in the calculation that
a+h
a
( x − a )2
dx = 1 h3 .
3
proof
Created by T. Madas
Created by T. Madas
Question 144
(***+)
y
y = x2 − 4 x + 8
M
x
O
The figure above shows the curve with equation
y = x2 − 4x + 8 , x ∈ » .
The point M is the minimum point of the curve.
Find the area of the shaded region, bounded by the curve, the y axis and the straight
line segment from O to M .
MP1-P , area = 20
3
Created by T. Madas
Created by T. Madas
Question 145
(***+)
The curve C has equation
y = x3 + 2 x 2 − 7 , x ∈ » .
The point P lies on C where x = 2 .
a) Find an equation of the tangent to C at P .
The tangent to C at P meets C again at the point Q .
b) Show that the coordinates of Q are ( −6, −151) .
y = 20 x − 31
Created by T. Madas
