Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For
a
>
0
a>0
a
>
0
, define
f
a
(
x
)
=
ln
x
−
a
x
f_a(x)=\ln x - a x
f
a
(
x
)
=
ln
x
−
a
x
. For which values of
a
a
a
does the equation
f
a
(
x
)
=
0
f_a(x)=0
f
a
(
x
)
=
0
have at least one solution in the interval
(
1
,
e
)
(1,e)
(
1
,
e
)
? a)
0
<
a
≤
1
e
0<a\le \dfrac{1}{e}
0
<
a
≤
e
1
b)
0
<
a
<
1
e
0<a<\dfrac{1}{e}
0
<
a
<
e
1
c)
1
e
<
a
<
1
\dfrac{1}{e}<a<1
e
1
<
a
<
1
d)
1
≤
a
<
e
1\le a<e
1
≤
a
<
e
Browse the problem library