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Bài tập CALCULUS 57
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Created by T. Madas
Question 200
(****)
f ( x ) = x2 +
16
, x ≠ 0.
x
The curve C has equation y = f ( x ) .
Show that C has two turning points, of which one is stationary, and the other is a non
stationary point of inflection.
Determine the exact coordinates of each point.
point of inflection at
Created by T. Madas
( 3 −16,0) , min ( 2,12)
Created by T. Madas
Question 201
(****)
y
M
y = 8x − x2
O
A
x
The figure above shows the quadratic curve with equation
y = 8x − x2 , x ∈ » .
The point M is the maximum point of the curve and the point A is one of the curve’s
x intercepts.
Find the exact area of the shaded region, bounded by the curve, the x axis and the
straight line segment from A to M .
C2J , area = 224
3
Created by T. Madas
Created by T. Madas
Question 202
(****)
The point P , whose x coordinate is 1 , lies on the curve with equation
4
y=
k + 4x x
, x∈» , x > 0 ,
7x
where k is a non zero constant.
a) Determine, in terms of k , the gradient of the curve at P .
The tangent to the curve at P is parallel to the straight line with equation
44 x + 7 y − 5 = 0 .
b) Find an equation of the tangent to the curve at P .
MP1-Q ,
dy
dx
Created by T. Madas
=
x = 14
4 − 16k
, 44 x + 7 y = 25
7
