The curve is given by and

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

Problem

The curve is given by

x=2e^{t}

and

y=e^{2t}-t

. At the point

(2e,\,e^{2}-1)

on the curve, which statement about concavity is correct? (a) The curve is concave down at the point. (b) The tangent line is vertical at the point, so concavity is undefined. (c) The curve is concave up at the point. (d) The second derivative is zero at the point, indicating a possible point of inflection.

Related theory

Curve Analysis
Advanced Differentiation

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