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Mathematics
Mathematics
Problem
Consider the curve
x
=
t
2
,
y
=
t
4
+
k
t
x=t^{2},\;y=t^{4}+kt
x
=
t
2
,
y
=
t
4
+
k
t
where
k
k
k
is a real constant. (i) Find the value of
t
t
t
(in terms of
k
k
k
) at which the curve can have an inflection point. (ii) Determine all real values of
k
k
k
for which such an inflection point actually exists.
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