The curve defined parametrically by and is considered at

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

Problem

The curve defined parametrically by x(t)=t2x(t)=t^{2} and y(t)=t3y(t)=t^{3} is considered at t=−1t=-1. Which statement best describes its concavity at that point? (a) The concavity cannot be determined because dxdt=0\dfrac{dx}{dt}=0 at t=−1t=-1. (b) The curve is concave down because d2ydx2<0\dfrac{d^{2}y}{dx^{2}}<0 at t=−1t=-1. (c) The curve is concave up because d2ydx2>0\dfrac{d^{2}y}{dx^{2}}>0 at t=−1t=-1. (d) The point is an inflection point because d2ydx2=0\dfrac{d^{2}y}{dx^{2}}=0 at t=−1t=-1.

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