For the parametric curve ,

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

Problem

For the parametric curve x=f(t)x=f(t), y=g(t)y=g(t), which of the following gives the correct condition for a horizontal tangent at t=t0t=t_0? (a) dxdt=0\frac{dx}{dt}=0 and dydt≠0\frac{dy}{dt}\ne0 (b) dydt=0\frac{dy}{dt}=0 and dxdt≠0\frac{dx}{dt}\ne0 (c) dydt=0\frac{dy}{dt}=0, regardless of dxdt\frac{dx}{dt} (d) dxdt=0\frac{dx}{dt}=0 and dydt=0\frac{dy}{dt}=0

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