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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 178

A curve is defined parametrically by

x=t2+1,y=t3−3tx=t^2+1,\qquad y=t^3-3tx=t2+1,y=t3−3t, where t>0t>0t>0.

a.

Find dydx\dfrac{dy}{dx}dxdy​ in terms of ttt.

[3]
b.

Show that

d2ydx2=3(t2+1)4t3\dfrac{d^2y}{dx^2}=\dfrac{3(t^2+1)}{4t^3}dx2d2y​=4t33(t2+1)​.

[3]
c.

Hence classify the stationary point corresponding to t=1t=1t=1.

[2]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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