Consider the curve

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the curve r(t)=⟨t2+1,  3t−t2⟩\mathbf r(t)=\langle t^{2}+1,\;3t-t^{2}\rangle. For which value of tt is the tangent line to the curve parallel to the vector ⟨1,1⟩\langle 1,1\rangle? (a) t=0t=0 (b) t=12t=\dfrac{1}{2} (c) t=34t=\dfrac{3}{4} (d) t=1t=1

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