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Bài tập CALCULUS 81
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Created by T. Madas
Question 270
(****+)
A curve C and a straight L have respective equations
C : y = 4 x2 − 6 x + 3
and
L : 2x − 4 y + 3 = 0 .
Show that L is a normal to C , at some point.
MP1-W , proof
Created by T. Madas
Created by T. Madas
Question 271
(****+)
A curve C and a straight line L have respective equations
3
1
C : y = ax 2 − bx 2
and
L : y = 8 x − 32 ,
where a and b are non zero constants.
Given that L is a tangent to C at the point where x = 4 is, determine the value of a
and the value of b .
MP1-U , a = 4, b = 16
Created by T. Madas
Created by T. Madas
Question 272
(****+)
The figure above shows a solid prism, which is in the shape a right semi-circular
cylinder.
The total surface area of the 4 faces of the prism is
3
27π .
Given that the measurements of the prism are such so that its volume is maximized,
find in exact simplified form the volume of the prism.
SYN-E , Vmax =
Created by T. Madas
π
π +2
