The curve depends on the real parameter

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The curve

x=t^{2},\;y=t^{3}+at

depends on the real parameter

a

. A horizontal tangent occurs at some non-zero value of

t

if and only if (a)

a=0

(b)

a>0

(c)

a<0

(d)

a

can be any real number