Alevel_C1C2
Alevel_C1C2
Alevel_C1C2
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4. (a) y = (3x + 5)(2x – 3) B1<br />
(b)<br />
(c)<br />
( )<br />
5<br />
(0, -15), −<br />
3 , 0 , 3 2 , 0<br />
( ) A3 (4)<br />
dy<br />
= 12x<br />
+ 1 If<br />
dx<br />
y = 0, then x =<br />
1<br />
−<br />
dx 12<br />
M2 A1<br />
2<br />
d y<br />
12<br />
2<br />
dx − 1<br />
12 , − 1<br />
( ,<br />
12 )<br />
− 361<br />
24<br />
B1 A1 (5)<br />
y<br />
– 5 3<br />
O 3<br />
2<br />
x<br />
B2 (2)<br />
–15<br />
11<br />
5. Let A = xy 2 , substitute x = y + 9 in A = xy 2 B1<br />
A = y 3 + 9y 2<br />
B1oe<br />
dA<br />
dy<br />
2<br />
2<br />
= 3y<br />
+ 18y<br />
= 0, then y = 0 or y = -6 M2oe<br />
d A<br />
2<br />
= 6y<br />
+ 18 and d 2<br />
A < 0 at y = -6 M2oe<br />
dy<br />
2<br />
dy<br />
Therefore A is max. at y = -6, x = 3<br />
A2<br />
Maximum value of xy 2 is 108<br />
A1<br />
9<br />
© Oxford University Press 2008<br />
Core C2
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