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Bài tập CALCULUS 60
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Created by T. Madas
Question 209
(****)
y
C
y = 22 − 5 x −
4
x
x
R
O
A
B
D
The figure above shows part of the curve with equation
y = 22 − 5 x −
4
, x>0
x
The curve meets the x axis at A and B . The point C lies on the curve where x = 1 .
a) Verify that the coordinates of B are ( 4,0 ) .
b) Find an equation of the tangent to the curve at C .
The tangent to the curve at C crosses the x axis at the point D .
The finite region R , shown shaded in the above figure, is bounded by the curve, the
tangent to the curve at C and the x axis.
c) Determine the exact area of R .
(
)
SYN-Q , y + 3 x = 16 , D 16 ,0 , area = 23
3
3
Created by T. Madas
Created by T. Madas
Question 210
(****)
y=
a) Find an expression for
b) Show that the value of
d2y
dx 2
d2y
dx
2
1 − x3
, x ≠ 0.
x
.
where
dy
= 0 , is −6 .
dx
d2y
dx
Created by T. Madas
2
= 2 x −3 − 2
Created by T. Madas
Question 211
(****)
The curve C has equation
y = 2x , x ≥ 0
Find an equation of the normal to C at the point where x = 2 , giving the answer in
the form y = mx + c , where m and c are constants.
MP1-J , y = 6 − 2 x
Created by T. Madas
