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Mathematics
Problem
Let
x
=
t
3
+
k
t
x=t^{3}+kt
x
=
t
3
+
k
t
and
y
=
t
2
+
1
y=t^{2}+1
y
=
t
2
+
1
, where
k
k
k
is a constant. If the slope
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at
t
=
1
t=1
t
=
1
is
1
1
1
, determine the value of
k
k
k
. a)
k
=
1
k = 1
k
=
1
b)
k
=
−
1
k = -1
k
=
−
1
c)
k
=
−
2
k = -2
k
=
−
2
d)
k
=
−
5
k = -5
k
=
−
5
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