Let and for . Classify the concavity of the curve at (concave up or concave…

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

Problem

Let

x=\tan t

and

y=\tan^{2}t

for

-\frac{\tau}{4} < t < \frac{\tau}{4}

. Classify the concavity of the curve at

t=\tfrac{\pi}{6}

(concave up or concave down).