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Bài tập CALCULUS 40
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Created by T. Madas
Question 149
(***+)
(
)
f ( x ) = x 18 x 2 + 35 x − 45 , x ≥ 0 .
a) Find a simplified expression for f ′ ( x ) .
b) Show clearly that
f ′( x) =
15 ( 3 x − 1)( 2 x − 3)
2 x
.
3
f ′ ( x ) = 45 x 2 +
Created by T. Madas
105 12 45 − 12
x − x
2
2
Created by T. Madas
Question 150
(***+)
y
y = 2x +
1
x
B
A
x
O
The figure above shows part of the curve C , with equation
y = 2x +
1
, x≠0
x
The point A lies on C where x = 1 .
2
a) Find an equation of the normal to C at A .
The normal meets the curve again at the point B .
b) Determine the exact coordinates of B .
(
C1N , 2 x − 4 y + 11 = 0 , B 4 , 41
3 12
Created by T. Madas
)
Created by T. Madas
Question 151
(***+)
y
B
O
A
x
The figure above show the graph of the curve C with equation
2
y = x 1 − x 3 , x ∈ » , x ≥ 0 .
The curve meets the coordinate axes at the origin and at the point A (1,0 ) .
The two tangents to C at the origin O and at the point A , meet at the point B .
a) Calculate the value of
dy
at O , and hence write down an equation of the
dx
tangent to C at O .
b) Show that an equation of the tangent to C at A is
2x + 3 y = 2
c) Determine the area of the finite region bounded by C and the tangents to C at
O and at A .
SYN-H , y = x , area = 3
40
Created by T. Madas
