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Byju's Answer
Standard XII
Mathematics
Local Maxima
Find the maxi...
Question
Find the maximum and minimum value
f
(
x
)
=
x
50
−
x
20
in the interval
[
0
,
1
]
.
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Solution
f
(
x
)
=
x
50
−
x
20
in interval
[
0
,
1
]
f
′
(
x
)
=
50
x
49
−
20
x
19
(for critical points)
f
′
(
x
)
=
0
50
x
49
=
20
x
19
x
30
=
2
5
x
=
±
(
2
5
)
1
/
30
Now, maximum value
f
[
(
2
5
)
1
/
30
]
=
(
2
5
)
5
/
3
−
(
2
5
)
2
/
3
=
(
2
5
)
2
/
3
[
(
2
5
)
3
−
1
]
=
−
117
125
(
2
5
)
2
/
3
Minimum value,
f
[
−
(
2
5
)
1
/
30
]
=
−
(
2
5
)
5
/
3
+
(
2
5
)
2
/
3
=
(
2
5
)
2
/
3
[
(
2
5
)
3
−
1
]
=
−
133
125
(
2
5
)
2
/
3
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The maximum and minimum values of f (x) = x
50
-x
20
in the interval [0, 1] are