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Byju's Answer
Standard XII
Mathematics
Range
The minimum v...
Question
The minimum value of the function
6
x
+
3
x
+
6
−
x
+
3
−
x
+
2
is
Open in App
Solution
Given
f
(
x
)
=
6
x
+
3
x
+
6
−
x
+
3
−
x
+
2
=
(
6
x
+
6
−
x
)
+
(
3
x
+
3
−
x
)
+
2
=
(
6
x
+
1
6
x
)
+
(
3
x
+
1
3
x
)
+
2
Using A.M.-G.M. inequality,
(
6
x
+
1
6
x
)
≥
2
,
(
3
x
+
1
3
x
)
≥
2
∴
f
(
x
)
≥
6
Range of the function is
[
6
,
∞
)
Thus the minimum value is
6
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0
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