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Mathematics
Problem
Let
k
>
0
k>0
k
>
0
be a constant and let
f
(
x
)
=
e
k
x
f(x)=e^{kx}
f
(
x
)
=
e
k
x
on the interval
[
0
,
1
]
[0,1]
[
0
,
1
]
. Determine, in terms of
k
k
k
, the value of
c
c
c
in
(
0
,
1
)
(0,1)
(
0
,
1
)
at which
f
′
(
c
)
f'(c)
f
′
(
c
)
equals the average rate of change of
f
f
f
over
[
0
,
1
]
[0,1]
[
0
,
1
]
.
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