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Mathematics
Mathematics
Problem
Consider
F
(
x
)
=
k
ln
∣
x
∣
−
1
x
+
C
F(x)=k\ln|x|-\dfrac{1}{x}+C
F
(
x
)
=
k
ln
∣
x
∣
−
x
1
+
C
, where
k
k
k
is a constant and
x
≠
0
x\ne 0
x
=
0
. For which value of
k
k
k
does
F
′
(
x
)
=
1
x
2
F'(x)=\dfrac{1}{x^{2}}
F
′
(
x
)
=
x
2
1
for all
x
≠
0
x\ne 0
x
=
0
? a)
k
=
2
k=2
k
=
2
b)
k
=
1
k=1
k
=
1
c)
k
=
0
k=0
k
=
0
d)
k
=
−
1
k=-1
k
=
−
1
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