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Mathematics
Mathematics
Problem
If the function
f
(
x
)
=
a
x
e
b
x
2
f(x) = ax e^{bx^2}
f
(
x
)
=
a
x
e
b
x
2
have the maximum value
f
(
2
)
=
1
f(2) = 1
f
(
2
)
=
1
then (a)
a
=
e
2
a = \frac{\sqrt{e}}{2}
a
=
2
e
and
b
=
−
1
8
b = \frac{-1}{8}
b
=
8
−
1
(b)
a
=
−
e
2
a = \frac{-\sqrt{e}}{2}
a
=
2
−
e
and
b
=
1
8
b = \frac{1}{8}
b
=
8
1
(c)
a
=
1
8
a = \frac{1}{8}
a
=
8
1
and
b
=
e
2
b = \frac{\sqrt{e}}{2}
b
=
2
e
(d)
a
=
−
e
2
a = \frac{-\sqrt{e}}{2}
a
=
2
−
e
and
b
=
−
1
8
b = \frac{-1}{8}
b
=
8
−
1
(a)
a
=
e
2
a = \frac{\sqrt{e}}{2}
a
=
2
e
and
b
=
−
1
8
b = \frac{-1}{8}
b
=
8
−
1
(b)
a
=
−
e
2
a = \frac{-\sqrt{e}}{2}
a
=
2
−
e
and
b
=
1
8
b = \frac{1}{8}
b
=
8
1
(c)
a
=
1
8
a = \frac{1}{8}
a
=
8
1
and
b
=
e
2
b = \frac{\sqrt{e}}{2}
b
=
2
e
(d)
a
=
−
e
2
a = \frac{-\sqrt{e}}{2}
a
=
2
−
e
and
b
=
−
1
8
b = \frac{-1}{8}
b
=
8
−
1
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