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ISI B.Math Entrance Exam
2009 ISI B.Math Entrance Exam
9
B.Math(Hons.) Admission Test 2009 problem 9
B.Math(Hons.) Admission Test 2009 problem 9
Source:
April 9, 2012
inequalities
triangle inequality
function
Problem Statement
Let
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x)=ax^2+bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are real numbers. Suppose
f
(
−
1
)
,
f
(
0
)
,
f
(
1
)
∈
[
−
1
,
1
]
f(-1),f(0),f(1) \in [-1,1]
f
(
−
1
)
,
f
(
0
)
,
f
(
1
)
∈
[
−
1
,
1
]
. Prove that
∣
f
(
x
)
∣
≤
3
2
|f(x)|\le \frac{3}{2}
∣
f
(
x
)
∣
≤
2
3
for all
x
∈
[
−
1
,
1
]
x \in [-1,1]
x
∈
[
−
1
,
1
]
.
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