Consider the curve defined by and

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

Problem

Consider the curve defined by

x=t^{2}-\ln t

and

y=e^{t}

(t>0)

. At which value of

t

does the curve have a vertical tangent? (a)

t=\dfrac12

(b)

t=1

(c)

t=\dfrac{1}{\sqrt{2}}

(d)

t=\sqrt[3]{\dfrac12}