7

x 1
y
x
1
x(1)
x
1
dy
2 x
dx
x
dy
for turning point 0
dx
1
0 x x
1
2 x
2x
x 1
2 x
0 = 2x – x – 1
0 = x – 1
x = 1
11
2 2
y(1) = or 2or
2
1 1 1
turning point are (1,2) and (1, -2)
X LHS 1 RHS
dy - 0 +
dx
Min
When x x
Or
X LHS 1 RHS
dy + 0 -
dx
When
x
x
Max
Hence (1,2) is minimum point while (1, -2) is
maximum point
Asymptotes vertical x 0
x = 0
Slanting
x
y =
x
x
1
x
1
x or y 2 = x
x 1
intercept when y = 0 0 =
x
x = -1 is outside the limit when x = 4
4 1
5
y = 2.5 or 2.5(1dp).
4 2
y
(0,0)
(1, 2)
Figure 135
Figure 135 is a sketch of the curve y = t + t
1
and x = t 2 .
(1, -2)
y
Figure 136
x =1
Area of element shaded = 2y x (See figure
136)
Area required =
4 1
4
x 1
2 dx
x
1
4 1 3
2
2
x dx x
1
1
1
2
y
y
2 ydx
dx
x =4
(4, 2.5)
x
(y = x)
(4, -2.5)
x
250