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Bài tập CALCULUS 58
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Created by T. Madas
Question 203
(****)
y
y = 1 x2 − 2 x + 6
2
P
L1
R
Q
L2
O
x
The figure above shows the graph of the curve C with equation
y = 1 x2 − 2 x + 6 .
2
The point P is the point where C meets the y axis so that the straight line L1 is the
normal to C at P .
a) Find an equation for L1 .
( )
The point Q 3, 9 lies on C and the straight line L2 is the normal to C at Q .
2
The finite region R , shown shaded in the figure above, is bounded by L1 , L2 and C .
b) Find the area of R .
SYN-J , y = 1 x + 6 , 15
4
2
Created by T. Madas
Created by T. Madas
Question 204
(****)
6x
L
8x
The figure above shows a triangular prism with a volume of 960 cm3 .
The triangular faces of the prism are right angled with a base 8 x cm and a height of
6 x cm . The length of the prism is L cm .
a) Show that the surface area of the prism, A cm 2 , is given by
A = 48 x 2 +
960
.
x
b) Determine an exact value of x for which A is stationary and show that this
value of x minimizes A .
c) Show further that the minimum surface area of the prism is 144 3 100 cm 2 .
SYN-Z , x = 3 10 ≈ 2.15
Created by T. Madas
Created by T. Madas
Question 205
(****) non calculator
y=
Show that the value of
d2y
dx
2
1 2
− 3 , x ∈ » , x > 0 .
3 xx
where x = 2 , is
2
.
16
proof
Created by T. Madas
