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Bài tập CALCULUS 79
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Created by T. Madas
Question 264
(****+)
y
y = 3 8 x − 27
y =1
O
x
The figure above shows the curve C with equation
y = 3 8 x − 27 , x ∈ » .
The finite region R , shown shaded in the figure, is bounded by C , the y axis and the
straight line with equation y = 1 .
When the lengths are measured in m , R models the design of a yacht rudder.
Show that the area of the yacht rudder is 11 m 2 .
SYN-B , proof
Created by T. Madas
Created by T. Madas
Question 265
(****+)
The curve C has equation
y=
(
x3 5 x x − 128
x
) , x∈» ,
x>0.
dy d 2 y
d3y
a) Determine expressions for
,
and
.
dx dx 2
dx3
b) Show that the y coordinate of the stationary point of C is −k 3 4 , where k is
a positive integer.
c) Evaluate
d2y
at the stationary point of C .
dx 2
Give the answer in terms of 3 2 .
d) Find the value of
MP1-M ,
d3y
dx3
at the point on C , where
d2y
dx 2
=0.
3
1
dy
d2y
d3y
− 12
2
2 ,
= 20 x3 − 320 x 2 ,
=
60
x
−
480
x
=
120
x
−
240
x
,
dx
dx 2
dx3
k = 3072 , 960 3 2 , 360
Created by T. Madas
Created by T. Madas
Question 266
(****+)
Use differentiation to establish the number of real solutions of the equation
3 x 4 − 4 x3 − 12 x 2 + 15 = 0 .
You are not expected to solve the equation.
MP1-N , 2 solutions
Created by T. Madas
