For a curve described parametrically by with differentiable and

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

Problem

For a curve described parametrically by x=f(t),  y=g(t)x=f(t),\;y=g(t) with differentiable ff and gg, which one of the following conditions guarantees that the tangent at t=t0t=t_{0} is horizontal? (a) f′(t0)=g′(t0)f'(t_{0})=g'(t_{0}) (b) f′(t0)=0,  g′(t0)≠0f'(t_{0})=0,\;g'(t_{0})\neq0 (c) g′(t0)=0,  f′(t0)≠0g'(t_{0})=0,\;f'(t_{0})\neq0 (d) g′(t0)=0g'(t_{0})=0

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