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Lebl-Basic-Analysis-I
· Problem 3.2.11
Continuous Functions
Mathematics · continuous-functions
Problem
Let
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be continuous. Suppose
f
(
c
)
>
0
f(c) > 0
f
(
c
)
>
0
. Show that there exists an
α
>
0
\alpha > 0
α
>
0
such that for all
x
∈
(
c
−
α
,
c
+
α
)
x \in (c - \alpha, c + \alpha)
x
∈
(
c
−
α
,
c
+
α
)
, we have
f
(
x
)
>
0
f(x) > 0
f
(
x
)
>
0
.
Related theory
Characteristic Functions And Moment Generating Functions
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