For the curve ,

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For the curve x=t2−4tx = t^{2}-4t, y=t3−6ty = t^{3}-6t, it is observed that d2ydx2\dfrac{d^{2}y}{dx^{2}} is positive for t<2t<2, negative for t>2t>2, and zero at t=2t=2. Which one of the following statements about the point corresponding to t=2t=2 is correct? (a) The curve attains a local maximum ordinate yy at this point. (b) The tangent at this point is horizontal. (c) The point is an inflection point of the curve. (d) The curve is concave upward at this point only.

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