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Byju's Answer
Standard XII
Mathematics
Global Maxima
If the greate...
Question
If the greatest value of the function
f
(
x
)
=
1
4
x
4
−
2
3
x
3
−
3
2
x
2
+
2
;
x
ϵ
[
−
2
,
4
]
is M, then find the value of [M]
(where [ ] denotes greatest integer function.)
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Solution
f
(
x
)
=
x
4
4
−
2
x
3
3
−
3
x
2
2
+
2
f
′
(
x
)
=
x
3
−
2
x
2
−
3
x
=
x
(
x
−
3
)
(
x
+
1
)
Maxima at
x
=
−
2
f
(
0
)
=
2
f
(
−
2
)
=
4
+
16
3
−
6
+
2
=
16
3
f
(
4
)
=
64
−
128
3
−
24
+
2
=
−
2
3
M
=
[
16
3
]
=
5
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