Find the minimum value of X^50+50/x..............please solve this......
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f(x)=x
50
−x
20
in interval [0,1]
f
′
(x)=50x
49
−20x
19
(for critical points)
f
′
(x)=0
50x
49
=20x
19
x
30
=
5
2
x=±(
5
2
)
1/30
Now, maximum value f
⎣
⎢
⎡
(
5
2
)
1/30
⎦
⎥
⎤
=(
5
2
)
5/3
−(
5
2
)
2/3
=(
5
2
)
2/3
⎣
⎢
⎡
(
5
2
)
3
−1
⎦
⎥
⎤
=−
125
117
(
5
2
)
2/3
Minimum value, f
⎣
⎢
⎡
−(
5
2
)
1/30
⎦
⎥
⎤
=−(
5
2
)
5/3
+(
5
2
)
2/3
=(
5
2
)
2/3
⎣
⎢
⎡
(
5
2
)
3
−1
⎦
⎥
⎤
=−
125
133
(
5
2
)
2/3
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