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Bài tập CALCULUS 27
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Created by T. Madas
Question 103
(***+)
y
y = x3 − 9 x 2 + 24 x + 9
A
L
x
O
The figure above shows the graph of the curve C with equation
y = x3 − 9 x 2 + 24 x + 9 .
The straight line L is the normal to C at the point A , whose x coordinate is 5 .
a) Show that an equation of L is
x + 9 y = 266 .
b) Show further that the area of the finite region bounded by C , L and the y axis
is approximately 20 square units.
MP1-B , proof
Created by T. Madas
Created by T. Madas
Question 104
(***+)
The curve C has equation
(
y = 1+ x
a) Find an expression for
)
2
, x≥0.
dy
.
dx
The straight line L with equation
2 y = 3x + 6
is a tangent to C at the point P .
b) Use a calculus method to determine the coordinates of P .
C1X ,
Created by T. Madas
dy
1
= 1+
, P ( 4,9 )
dx
x
Created by T. Madas
Question 105
(***+)
y=
x2 + 4
, x ≠ 0.
4x
Find the range of values of x for which y is increasing.
C2W , x < −2 ∪ x > 2
Created by T. Madas
