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Byju's Answer
Standard XII
Mathematics
Strictly Increasing Functions
Find the grea...
Question
Find the greatest and the least values of the following function.
f
(
x
)
=
2
x
3
−
9
x
2
+
12
x
on the interval
[
0
,
3
]
.
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Solution
f
(
x
)
=
2
x
3
−
9
x
2
+
12
x
f
′
(
x
)
=
6
x
2
−
18
x
+
12
=
0
⇒
(
x
−
1
)
(
x
−
2
)
=
0
x
=
1
,
2
f
′′
(
x
)
=
(
2
x
−
3
)
6
f
′′
(
1
)
=
−
6
<
0
hence
f
(
1
)
=
5
is maximum
f
′′
(
2
)
=
6
>
0
hence
f
(
2
)
=
4
is minimum
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