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Byju's Answer
Standard XII
Mathematics
Second Derivative Test for Local Minimum
Which of the ...
Question
Which of the following function has extreme point(s)
A
All of the above.
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B
x
−
[
x
]
,
where
[
.
]
denotes the greatest integer function.
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C
log
10
x
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D
2
x
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Solution
The correct option is
B
x
−
[
x
]
,
where
[
.
]
denotes the greatest integer function.
For
y
=
2
x
⇒
d
y
d
x
=
2
x
⋅
ln
2
=
0
has no solution.
For
y
=
log
10
x
⇒
d
y
d
x
=
1
x
⋅
log
e
10
=
0
has no solution
For
y
=
x
−
[
x
]
=
{
x
}
;
From graph, we can see that every integral point is the point of local minima.
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Second Derivative Test for Local Minimum
Standard XII Mathematics
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