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Bài tập CALCULUS 64
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Created by T. Madas
Question 221
(****)
2c
h
r
The figure above shows solid right prism of height h cm .
The cross section of the prism is a circular sector of radius r cm , subtending an angle
of 2 radians at the centre.
a) Given that the volume of the prism is 1000 cm3 , show clearly that
S = 2r 2 +
4000
,
r
where S cm 2 is the total surface area of the prism.
b) Hence determine the value of r and the value of h which make S least, fully
justifying your answer.
C2P , r = 10 , h = 10
Created by T. Madas
Created by T. Madas
Question 222
(****)
A curve has equation
y = x2 − 6 x
3
x +2,
x∈» ,
x ≥ 0.
Find the coordinates of the stationary points of the curve and classify them as local
maxima, local minima or a points of inflexion.
MP1-X , local minimum at ( 8, −30 ) , local maximum at ( 0, 2 )
Created by T. Madas
Created by T. Madas
Question 223
(****)
y
5
y = 27 x − 8 x 2
P
O
x
The figure above shows the curve C with equation
5
y = 27 x − 8 x 2 , x ≥ 0
The curve meets the x axis at the origin O and at the point P .
a) Find the exact x coordinate of P .
b) Calculate the gradient of C at the point P .
dy
= − 81
x=9 ,
2
4 dx
Created by T. Madas
