Let and for .

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

x=e^{t}

and

y=t\,\ln t

for

t>1

. (i) Determine

\dfrac{d^{2}y}{dx^{2}}

in terms of

t

. (ii) Show that

\dfrac{d^{2}y}{dx^{2}}<0

for all

t>1

. (iii) What does the result of part (ii) imply about the curvature of the curve for

t>1

? State your answer clearly.