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Bài tập CALCULUS 06
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Created by T. Madas
Question 20
(**+)
The curve C has equation
y = − x 2 ( x + 1) , x ∈ » .
The curve meets the coordinate axes at the origin O and at the point A .
a) Sketch the graph of C , indicating clearly the coordinates of A .
b) Show that the straight line with equation
x + y +1 = 0 ,
is a tangent to C at A .
C1D , A ( −1, 0 )
Created by T. Madas
Created by T. Madas
Question 21
(**+)
y = 1 x ( x − 5)
2
y
2
O
5
6
x
A fish logo is generated by the curve C with equation
2
y = 1 x ( x − 5) , 0 ≤ x ≤ 6 ,
2
and its reflection in the x axis.
The curve C meets the x axis at the origin O and at the point ( 5,0 ) .
The finite region R is bounded by C , its reflection in the x axis and the straight line
with equation x = 6 .
Show that the area of R , shown shaded in the figure, is 54 square units.
MP1-N , proof
Created by T. Madas
Created by T. Madas
Question 22
(**+)
A curve C has equation
y = x3 − 3x 2 − 24 x − 1 , x ∈ » .
Find the range of values of x , for which y is increasing.
C2N , x < −2 ∪ x > 4
Question 23
(**+)
y = 4 x , x∈», x > 0 .
Show clearly that
d2y
dx
2
+
8 dy
= 0.
y 2 dx
C1O , proof
Created by T. Madas
