Consider the curve and

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Consider the curve x=t2−2tx=t^{2}-2t and y=t3−3t2y=t^{3}-3t^{2}. Which of the following ordered pairs of parameter values gives two distinct points on the curve whose tangent lines are parallel? (a) (−1,3)(-1,3) (b) (0,2)(0,2) (c) (−2,4)(-2,4) (d) (0,1)(0,1)

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