MathDB
Problems
Contests
Undergraduate contests
Putnam
Putnam 1938
A3
A3
Part of
Putnam 1938
Problems
(1)
Putnam 1938 A3
Source:
8/20/2021
A particle moves in the Euclidean plane. At time
t
t
t
(taking all real values) its coordinates are
x
=
t
3
ā
t
x = t^3 - t
x
=
t
3
ā
t
and
y
=
t
4
+
t
.
y = t^4 + t.
y
=
t
4
+
t
.
Show that its velocity has a maximum at
t
=
0
,
t = 0,
t
=
0
,
and that its path has an inflection at
t
=
0.
t = 0.
t
=
0.
Putnam