Consider the curve defined parametrically by and

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

Problem

Consider the curve defined parametrically by

x=3t^{2}+2

and

y=t^{3}-5t

. Answer the following parts. (i) State the relationship between

\dfrac{dy}{dx}

\dfrac{dy}{dt}

and

\dfrac{dx}{dt}

for a parametric curve. (ii) For the given curve, obtain an expression for

\dfrac{dy}{dx}

in terms of

t

and simplify your answer. (iii) Comment on the sign of

\dfrac{dy}{dx}

for

t>0

and explain what this signifies about the behaviour of the curve in that range.