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UPSC NDA Math Model Paper 10
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© examsnet.com
Question : 116
Total: 120
The function
f
(
x
)
=
x
3
−
3
x
2
+
6
is an increasing function for
0 < x < 2
x < 2
x > 2 or x < 0
all x ∈ R
Validate
Solution:
Given:
f
(
x
)
=
x
3
−
3
x
2
+
6
⇒
f
′
(
x
)
=
3
x
2
−
6
x
To be an increasing function
f
′
(
x
)
>
0
⇒
f
′
(
x
)
=
3
x
2
−
6
x
=
3
x
(
x
−
2
)
>
0
⇒
x
<
0
or
x
>
2
© examsnet.com
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