Oxford University MAT 2020 Solved Papers

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Question : 7 of 10

Marks: +1, -0

A cubic has equation

y=x^3+a x^2+b x+c

and has turning points at

(1,2)

and

(3, d)

for some

d

. What is the value of

d

?

-4,
$-2$ ,
0 ,
2 ,
4 .

Solution:

The turning points have

\;{ {d} y}/{ {d} x}=0

at

x=1

and at

x=3

, so

3+2 a+b=0

and

27+6 a+b=0

. Solve these for

a=-6, b=9

. Now

y=2

at

x=1

so

c=-2

. Then

y=-2

at

x=3

gives

d=-2

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