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Mathematics
Mathematics
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial function of degree 2 and
f
(
x
)
>
0
f(x) > 0
f
(
x
)
>
0
for all
x
∈
R
x \in \mathbb{R}
x
∈
R
. If
g
(
x
)
=
f
(
x
)
+
f
′
(
x
)
+
f
′
′
(
x
)
g(x) = f(x) + f'(x) + f''(x)
g
(
x
)
=
f
(
x
)
+
f
′
(
x
)
+
f
′′
(
x
)
, then for any
x
x
x
show that
g
(
x
)
>
0
g(x) > 0
g
(
x
)
>
0
.
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