For the curve

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

Problem

For the curve

x=e^{t},\; y=e^{-t}

, determine the value(s) of

t

where the tangent has slope

-1

. Also write the equation of the tangent line at each such point.