At a polar curve satisfies and

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

Problem

At θ=π2\theta=\dfrac{\pi}{2} a polar curve satisfies dydx=0\dfrac{dy}{dx}=0 and d2ydx2>0\dfrac{d^{2}y}{dx^{2}}>0. Which statement is most consistent with the behavior of the curve at that point? (a) The tangent is vertical and the curve is concave upward. (b) The tangent is horizontal and the curve is concave downward. (c) The tangent is horizontal and the curve is concave upward. (d) The tangent is vertical and the curve is concave downward.

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