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Bài tập CALCULUS 90
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Created by T. Madas
Question 297
(*****)
The points A and B are stationary points of the curve with equation
y = 2 x 3 + 3 x 2 − 12 x + k , x ∈ » ,
where k is a constant.
Given that y = 37 at the point of inflexion of the curve, show that the area of the
2
region bounded by the curve and the straight line through A and B is 5 1 .
16
SP-M , proof
Created by T. Madas
Created by T. Madas
Question 298
(*****)
A quadratic curve has equation
y = ax 2 + bx + c , a ≠ 0 ,
where a , b and c are constants.
The curve meets the x axis at A ( −2,0 ) and has a maximum point at B ( 0,1) .
The point C lies on the curve so that AB is perpendicular to BC .
Determine the area of the finite region bounded by the curve and the straight line
segment AC .
SP-U , proof
Created by T. Madas
Created by T. Madas
Question 299
(*****)
The rate of change, with respect to x , of the gradient of a curve is constant.
The curve passes through the points with coordinates (1, 2 ) and ( −3,0 ) , the gradient at
the former point being − 1 .
2
Show that the area of the finite region bounded between the curve and the straight line
125
with equation y = 2 x is
.
3
SP-A , proof
Created by T. Madas
