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Putnam
1975 Putnam
A3
A3
Part of
1975 Putnam
Problems
(1)
Putnam 1975 A3
Source: Putnam 1975
2/17/2022
Let
0
<
α
<
β
<
γ
∈
R
0<\alpha<\beta <\gamma\in \mathbb{R}
0
<
α
<
β
<
γ
∈
R
. Let
K
=
{
(
x
,
y
,
z
)
∈
R
3
∣
x
,
y
,
z
≥
0
and
x
β
+
y
β
+
z
β
=
1
}
K=\{(x,y,z)\in \mathbb{R}^{3}\;|\; x,y,z\geq 0\; \text{and}\; x^{\beta}+y^{\beta}+z^{\beta}=1\}
K
=
{(
x
,
y
,
z
)
∈
R
3
∣
x
,
y
,
z
≥
0
and
x
β
+
y
β
+
z
β
=
1
}
. Define
f
:
K
→
R
,
(
x
,
y
,
z
)
↦
x
α
+
y
β
+
z
γ
f:K\rightarrow \mathbb{R},\; (x,y,z)\mapsto x^{\alpha}+y^{\beta}+z^{\gamma}
f
:
K
→
R
,
(
x
,
y
,
z
)
↦
x
α
+
y
β
+
z
γ
. At what points of
K
K
K
does
f
f
f
assume its minimal and maximal values?
Putnam
maximum value