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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 23

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

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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