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Mathematics
Problem
Let
p
a
(
x
)
=
e
−
x
+
a
x
p_a(x)=e^{-x}+ax
p
a
(
x
)
=
e
−
x
+
a
x
be defined on
[
0
,
1
]
[0,1]
[
0
,
1
]
. Determine all real values of
a
a
a
such that the absolute minimum of
p
a
p_a
p
a
on this interval occurs at
x
=
0
x=0
x
=
0
.
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