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Mathematics
Mathematics
Problem
If the tangent to the curve,
y
=
f
(
x
)
=
x
log
e
x
y = f(x) = x \log_e x
y
=
f
(
x
)
=
x
lo
g
e
x
, (
x
>
0
x > 0
x
>
0
) at a point
(
c
,
f
(
c
)
)
(c, f(c))
(
c
,
f
(
c
))
is parallel to the line segment joining the points
(
1
,
0
)
(1, 0)
(
1
,
0
)
and
(
e
,
e
)
(e, e)
(
e
,
e
)
, then
c
c
c
is equal to: (a)
e
−
1
e
\frac{e-1}{e}
e
e
−
1
(b)
e
(
1
e
−
1
)
e^{\left(\frac{1}{e-1}\right)}
e
(
e
−
1
1
)
(c)
e
(
1
1
−
e
)
e^{\left(\frac{1}{1-e}\right)}
e
(
1
−
e
1
)
(d)
e
e
−
1
\frac{e}{e-1}
e
−
1
e
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