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Byju's Answer
Standard XII
Mathematics
Subset
f x = x3+ax2+...
Question
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
has a max. at
x
=
−
1
and min. at
x
=
3
. Determine the constants
a
,
b
,
c
.
A
∴
a
=
−
3
,
b
=
−
3
,
c
=
0.
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B
∴
a
=
−
3
,
b
=
−
9
,
c
=
3.
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C
∴
a
=
−
3
,
b
=
9
,
c
=
9.
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D
∴
a
=
3
,
b
=
9
,
c
=
−
3.
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Solution
The correct option is
B
∴
a
=
−
3
,
b
=
−
9
,
c
=
3.
Given
y
=
x
3
+
a
x
2
+
b
x
+
c
d
y
d
x
=
3
x
2
+
2
a
x
+
b
=
0
At
x
=
−
1
∴
3
−
2
a
+
b
=
0
∴
−
2
a
+
b
=
−
3
....(1)
At
x
=
3
27
+
6
a
+
b
=
0
∴
6
a
+
b
=
−
27
....(2)
Solving (1) and (2), we get
a
=
−
3
,
b
=
−
9
There is no condition for
c
, therefore
c
can assume any real value.
∴
a
=
−
3
,
b
=
−
9
,
c
ϵ
R
.
Suggest Corrections
1
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