For the curve :

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For the curve

x=e^{t},\;y=t-\ln t\;(t>0)

: (i) find the value(s) of

t

for which the tangent is horizontal; (ii) determine whether the curve has any vertical tangents.