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Bài tập CALCULUS 31
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Created by T. Madas
Question 116
(***+)
The curve C has equation y = f ( x ) given by
3
f ( x ) = 2 ( x − 2) , x ∈ » .
a) Sketch the graph of f ( x ) .
b) Find an expression for f ′ ( x ) .
The point P ( 3, 2 ) lies on C and the straight line l1 is the tangent to C at P .
c) Find an equation of l1 .
The straight line l2 is another tangent at a different point Q on C .
d) Given that l1 is parallel to l2 show that an equation of l2 is
y = 6x − 8 .
C1M , f ′ ( x ) = 6 x 2 − 24 x + 24 , y = 6 x − 16
Created by T. Madas
Created by T. Madas
Question 117
(***+)
r
h
A hollow container, made of thin sheet metal, is in the shape of a right circular cylinder,
which is open at one of its circular ends.
The container has radius r cm, height h cm and a capacity of 1500 cm3 .
a) Show that the surface area, A cm 2 , of the container is given by
A = π r2 +
3000
.
r
b) Determine the value of r for which A has a stationary value.
c) Show that the value of r found in part (b) gives the minimum value for A .
d) Calculate, to the nearest cm 2 , the minimum surface area of the container.
SYN-A , r ≈ 7.816 , Amin ≈ 576
Created by T. Madas
Created by T. Madas
Question 118
(***+)
y
4
y=
1
x2
1
x
O
The figure above shows part of the graph of the curve with equation
y=
1
x2
, x∈», x > 0 .
Find the area bounded by the curve, the y axis, and the straight lines with equations
y = 1 and y = 4 .
SYN-N , 2
Created by T. Madas
