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Putnam
1940 Putnam
A2
A2
Part of
1940 Putnam
Problems
(1)
Putnam 1940 A2
Source: Putnam 1940
2/22/2022
Let
A
,
B
A,B
A
,
B
be two fixed points on the curve
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
,
f
f
f
is continuous with continuous derivative and the arc
A
B
^
\widehat{AB}
A
B
is concave to the chord
A
B
AB
A
B
. If
P
P
P
is a point on the arc
A
B
^
\widehat{AB}
A
B
for which
A
P
+
P
B
AP+PB
A
P
+
PB
is maximal, prove that
P
A
PA
P
A
and
P
B
PB
PB
are equally inclined to the tangent to the curve
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
at
P
P
P
.
Putnam
calculus
derivative