Bài tập CALCULUS 22

Created by T. Madas
Question 85

(***+)

y

y = f ( x)

R
O

A

B

x

The figure above shows the graph of the curve with equation
4x − 8

x<5
.
f ( x) =  2
− x + 14 x − 33 x ≥ 5
The curve meets the x axis at the points A and B .
The finite region R , shown shaded in the figure above, is bounded by the curve and
the x axis.
Find the area of R .
C2Z , 90

Created by T. Madas


Created by T. Madas
Question 86

(***+)
y

R
C

Q

P
O

x

The figure above shows the curve C which meets the coordinates axes at the points P ,
Q and R .
Given the gradient function of C is given by

f ′( x) = 3 − 4x ,
and that f (1) = 2 f ( 2 ) , determine the coordinates of P , Q and R .

( )

C1E , P ( −1, 0 ) , P 5 , 0 , R ( 0,5 )
2

Created by T. Madas


Created by T. Madas
Question 87

(***+)

The curve C has equation

(

)

y = ( x − 1) x 2 + 4 x + 5 , x ∈ » .
a) Show that C meets the x axis at only one point.
The point A , where x = −1 , lies on C .

b) Find an equation of the normal to C at A .
The normal to C at A meets the coordinate axes at the points P and Q .

c) Show further that the area of the triangle OPQ , where O is the origin, is 12 1
4
square units.
C1J , 2 y = x − 7

Created by T. Madas