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Bài tập CALCULUS 62
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Created by T. Madas
Question 215
(****)
f ( x ) = ax 2 + bx + c , x ∈ » ,
where a , b and c are constants.
It is given that f ( x ) passes through the points ( 2,3) and ( −1,9 ) , and the curve has a
stationary point where x = 1 .
Determine the value of a , b and c ,
a = 2 , b = −4 , c = 3
Created by T. Madas
Created by T. Madas
Question 216
(****)
y
y = x 2 − 6 x + 10
A
O
x
B
The figure above shows the curve with equation
y = x 2 − 6 x + 10 , x ∈ » .
The point A , where x = 4 , lies on the curve.
The tangent to the curve at A , meets the y axis at B .
Determine the area of the finite region bounded by the curve, the tangent to the curve
at A and the y axis.
SYN-L , 64
3
Created by T. Madas
Created by T. Madas
Question 217
(****)
y
A
y =8 x +
R
16
x2
− 13
B
x
O
The figure above shows part of the curve with equation
y =8 x +
16
x2
− 13 , x > 0 .
The points A and B lie on the curve where x = 1 and x = 4 , respectively.
The finite region R is bounded by the curve, the straight line segment AB .
Determine the exact area of R .
C2H , area = 73
6
Created by T. Madas
