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Mathematics
Mathematics
Problem
Consider the curve
r
(
t
)
=
⟨
t
2
+
1
,
3
t
−
t
2
⟩
\mathbf r(t)=\langle t^{2}+1,\;3t-t^{2}\rangle
r
(
t
)
=
⟨
t
2
+
1
,
3
t
−
t
2
⟩
. For which value of
t
t
t
is the tangent line to the curve parallel to the vector
⟨
1
,
1
⟩
\langle 1,1\rangle
⟨
1
,
1
⟩
? a)
t
=
0
t=0
t
=
0
b)
t
=
1
2
t=\dfrac{1}{2}
t
=
2
1
c)
t
=
3
4
t=\dfrac{3}{4}
t
=
4
3
d)
t
=
1
t=1
t
=
1
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