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Bài tập CALCULUS 30
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Created by T. Madas
Question 113
(***+)
y
L
P
Q
O
y = 8 + 2 x − x2
R
x
The figure above shows the graph of a curve with equation
y = 8 + 2 x − x2 .
The curve meets the y axis at the point P , and the x axis at the points Q and R .
a) Determine the coordinates of P , Q and R .
The straight line L is the tangent to the curve at P .
b) Find an equation of L .
c) Show that the area of the finite region bounded by the curve, the tangent L and
the x axis is 20 .
3
MP1-G , P ( 0,8 ) , Q ( −2,0 ) , R ( 4,0 ) , y = 2 x + 8
Created by T. Madas
Created by T. Madas
Question 114
(***+)
On a given lorry journey the cost C , in pence per mile, is modelled by
C=
192 V 2
+
, V >6,
V 144
where V is the lorry’s average speed in metres per second.
a) Find the speed, in metres per second, for which the cost, in pence per mile, is
stationary.
b) Justify that this value of the speed minimizes the cost.
c) Hence determine the minimum cost of a 600 mile journey.
C2V , V = 24 , £72
Created by T. Madas
Created by T. Madas
Question 115
(***+)
A certain chemical industrial process is carried out at low temperatures.
The wastage cost £C during this chemical process and the average temperature T °C
are related by the equation
C=
36 2T 2
+
, T > 0.
T
3
Find the average temperature during which the wastage cost is increasing.
C2V , T > 3
Created by T. Madas
