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Mathematics
Mathematics
Problem
If
f
(
x
)
f(x)
f
(
x
)
is a quadratic expression such that
f
(
x
)
>
0
∀
x
∈
R
f(x) > 0 \forall x \in \mathbb{R}
f
(
x
)
>
0∀
x
∈
R
, and 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 prove that
g
(
x
)
>
0
∀
x
∈
R
g(x) > 0 \forall x \in \mathbb{R}
g
(
x
)
>
0∀
x
∈
R
.
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