0 f(x) has only one minimum." >
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AP and TS EAMCET Engineering Model Paper 17
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© examsnet.com
Question : 77
Total: 160
Let
f
(
x
)
=
a
0
+
a
1
x
2
+
a
2
x
4
+
.
.
.
+
a
n
x
2
n
be a polynomial in
x
∈
R
with
0
<
a
0
<
a
1
<
.
.
.
<
a
n
then
f
(
x
)
has
only one minimum
only one maximum
one maximum one minimum
neither maximum nor minimum
Validate
Solution:
f
(
x
)
=
a
0
+
a
1
x
2
+
a
2
x
4
+
.
.
.
+
a
n
x
2
n
f
′
(
x
)
=
2
a
1
x
+
4
a
2
x
3
+
.
.
.
+
2
n
a
n
x
2
n
−
1
f
′
′
(
x
)
=
2
a
1
+
12
a
2
x
2
+
.
.
.
+
2
n
(
2
n
−
1
)
a
n
x
2
n
−
2
f
′
(
x
)
=
0
x
=
0
f
"
(
x
)
=
2
a
1
>
0
f(x) has only one minimum.
© examsnet.com
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