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Bài tập CALCULUS 37
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Created by T. Madas
Question 138
(***+)
y
M
y = 4x − x2
O
A
x
The figure above shows the curve with equation
y = 4x − x2 , x ∈ » .
The point M is the maximum point of the curve and the point A is one of the x
intercepts of the curve.
Find the exact area of the shaded region, bounded by the curve and the straight line
segment joining A and M .
MP1-H , area = 4
3
Created by T. Madas
Created by T. Madas
Question 139
(***+)
The curve C has equation
y = x3 − 6 x 2 + 9 x .
a) Sketch the graph of C , indicating clearly the coordinates of the points where
the graph meets the coordinate axes.
b) Determine the exact value of the area of the finite region bounded by the curve
and the x axis .
( 0, 0 ) & ( 3, 0 ) ,
Question 140
area = 27
4
(***+) non calculator
The curve C has equation
y = x + x3 , x ≠ 0
Find the exact coordinates of the point on the curve where the gradient is 2 .
20
( 94 , 27
)
Created by T. Madas
Created by T. Madas
Question 141
(***+)
The curve C has equation
y = 4 x3 − 7 x − 1 , x ∈ » .
The point A lies on C where x = 1 .
a) Find an equation of the tangent to C at A .
The tangent to C at A meets C again at the point B .
b) Find the coordinates of B .
C1K , y = 5 x − 9 , B ( −2, −19 )
Created by T. Madas
