The parametric representation of a curve is x = t^ 2 e^ t

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

The parametric representation of a curve is

x = t^{2}e^{t},\qquad y = te^{2t},\qquad t> -1.

(i) Derive an expression for

\dfrac{dy}{dx}

in terms of

t

. (ii) Derive an expression for

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

in terms of

t

. (iii) Find all real values of

t

(if any) for which

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

, and classify the concavity of the curve in the intervals determined by these values.