Let be a real constant

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

p

be a real constant. The curve given by

x=t^{2}+1

and

y=t^{3}+p\,t

is required to be concave upward for every positive value of

t

. Which one of the following conditions on

p

guarantees this requirement? (a)

p<0

(b)

p\le 0

(c)

p>0

(d)

p<3