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Byju's Answer
Standard VII
Mathematics
Organization of Data
The least val...
Question
The least value of the function f(x) =
x
3
-
18
x
2
+
96
x
in the interval [0,9] is
(a) 126
(b) 135
(c) 160
(d) 0
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Solution
(
d
)
0
Given
:
f
x
=
x
3
-
18
x
2
+
96
x
⇒
f
'
x
=
3
x
2
-
36
x
+
96
For
a
local
maxima
or
a
local
minima
,
we
must
have
f
'
x
=
0
⇒
3
x
2
-
36
x
+
96
=
0
⇒
x
2
-
12
x
+
32
=
0
⇒
x
-
4
x
-
8
=
0
⇒
x
=
4
,
8
So
,
f
8
=
8
3
-
18
8
2
+
96
8
=
512
-
1152
+
768
=
128
f
4
=
4
3
-
18
4
2
+
96
4
=
64
-
288
+
384
=
160
f
0
=
0
3
-
18
0
2
+
96
0
=
0
f
9
=
9
3
-
18
9
2
+
96
9
=
729
-
1458
+
864
=
135
Hence, 0 is the minimum value in the range
0
,
9
.
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0
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