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Problem
Problem
If
H
(
x
0
)
=
0
H(x_0) = 0
H
(
x
0
)
=
0
for some
x
=
x
0
x = x_0
x
=
x
0
and
d
d
x
H
(
x
)
>
2
c
x
H
(
x
)
\frac{d}{dx} H(x) > 2cx H(x)
d
x
d
H
(
x
)
>
2
c
x
H
(
x
)
for all
x
≥
x
0
x \ge x_0
x
≥
x
0
, where
c
>
0
c > 0
c
>
0
, then prove that
H
(
x
)
H(x)
H
(
x
)
cannot be zero for any
x
>
x
0
x > x_0
x
>
x
0
.
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