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Bài tập CALCULUS 34
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Created by T. Madas
Question 128
(***+)
The curve C has equation
(
)
y = ( x − 2) x2 − 2 x − 3 , x ∈ » .
a) Sketch the graph of C , indicating the coordinates of any points where the curve
meets the coordinate axes.
b) Find an equation of the tangent to C at the point P , where P is the point
where C crosses the y axis.
The point Q lies on C so that the tangent to the curve at Q is parallel to the tangent to
the curve at P .
c) Determine the exact coordinates of Q .
( −1,0 ) , ( 2,0 ) , ( 3, 0 ) , ( 0,6 ) ,
Created by T. Madas
(
y = x + 6 , Q 8 , − 22
3 27
)
Created by T. Madas
Question 129
(***+) non calculator
f ( x) = 4 x − 3 x , x ≥ 0 .
Show clearly that
f ′ ( 64 ) =
11
.
48
proof
Question 130
(***+)
The curve C has equation
y = 2 x − x3 , x ≥ 0 .
Show that the equation of the tangent to C at the point where x = 2 , can be written as
y = 2 (2 − x)
proof
Created by T. Madas
Created by T. Madas
Question 131
(***+)
θ
x
x
A circular sector of radius x cm subtends an angle of θ radians at the centre.
The area of the sector is 36 cm 2 and its perimeter is P cm .
a) Show clearly that
P = 2x +
72
.
x
b) Find the minimum value of P , fully justifying the fact that it is a minimum.
c) Deduce the value of θ when P is minimum.
SYN-R , Pmin = 24 , θ = 2c
Created by T. Madas
