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Vojtěch Jarník IMC
1995 VJIMC
Problem 2
even function has extremum at 0
even function has extremum at 0
Source: VJIMC 1995 1.2
October 27, 2021
function
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be an even twice differentiable function such that
f
′
′
(
0
)
≠
0
f''(0)\ne0
f
′′
(
0
)
=
0
. Prove that
f
(
x
)
f(x)
f
(
x
)
has a local extremum at
x
=
0
x=0
x
=
0
.
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