Cambridge International Mathematics

726 ANSWERS

b¼ 5 : 17 c¼(3: 72 ,¡124)

d

elocal maximum at¼(¡ 0 : 470 , 4 :44)

local minimum at(¡ 1 ,4)

f xy xy

030 : 6 ¡ 5 : 32

0 : 12 : 20 0 : 7 ¡ 7 : 59

0 : 21 : 18 0 : 8 ¡ 10 : 1

0 : 3 ¡ 0 :07 0: 9 ¡ 12 : 9

0 : 4 ¡ 1 :57 1: 0 ¡ 16

0 : 5 ¡ 3 : 31

5a if(x)=^4

x¡ 2

ii x=2,y=0

iii nox-intercept

y-intercept¡ 2

iv no turning points

exist

bif(x)=2¡

3

x+1

ii x=¡ 1 ,y=2

iii x-intercept^12

y-intercept¡ 1

iv no turning points

exist

cif(x)=2x¡ 3 iiy=¡ 3

iiix-intercept¼ 1 : 58

y-intercept¡ 2

iv no turning points

exist

dif(x)=2x+

1

x

iix=0, y=2x

iii no intercepts exist

iv local maximum

at¼(¡ 0 : 707 ,¡ 2 :83)

local minimum

at¼(0: 707 , 2 :83)

eif(x)=^4 x

x^2 ¡ 4 x¡ 5

iix=¡ 1 ,x=5,

y=0

iii x- andy-intercepts

are both 0

iv no turning points

exist

fif(x)=3¡x+2 iiy=2

iii nox-intercepts,

y-intercept is 3

iv no turning points

exist

gif(x)=

x^2 ¡ 1

x^2 +1

ii y=1

iii x-intercepts§ 1

y-intercept¡ 1

iv minimum turning

point at(0,¡1)

hif(x)=x

(^2) +1
x^2 ¡ 1
ii x=¡ 1 ,x=1
y=1
iii nox-intercepts
y-intercept¡ 1
iv maximum turning
point at(0,¡1)
iif(x)=^2
x+3
2 x+1
ii y=1,y=3
iii nox-intercepts
y-intercept 2
iv no turning points
exist
6a x f(x)
¡ 2 ¡ 3 : 75
¡ 1 ¡ 0 : 5
01
11
20
3 ¡ 1
40
57
b
c ¼¡ 0 : 767 , 2 , 4
d maximum turning point at¼(0: 485 , 1 :16)
minimum turning point at¼(3: 21 ,¡ 1 :05)
y
-1 x
Qw
y¡=¡2
x¡=¡-1
1
() 2 3
fx= -x+
3
()1 -16,
()-2 ¡17,
y
x
O
2
()^4
fx=x-
-2
y
x
x¡=¡2
O
y
x
»1.58
-2
y¡=¡-3
f(x)= 2 x- 3
O
y
x
yx¡=¡2
x¡=¡0
O
fx x x
()= 2 +^1
()0 707 ¡2 83.,.
(-0 707 -2 83.,.)
y
x
x¡=¡5
x¡=¡-1
y¡=¡0 O
y
x
y¡=¡2^3
O
y
x
y¡=¡1
-1 1
()0 -1,
O
y
-1 x
x¡=¡-1 x¡=¡1
y¡=¡1
O
y
x
y¡=¡3
y¡=¡1
2
O
(-2 -3, Er)
()5 ¡7,
»¡-0 767.
24
y
O x
f(x)= 2 x-x^2
1
()0.485,¡1.16
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\726IB_IGC1_an.CDR Thursday, 20 November 2008 4:53:40 PM PETER