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5 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2 · Question 1(a)(i)a)

Given the curve y = x^2 e^x.

Find \frac{\mathrm{d}y}{\mathrm{d}x} and \frac{\mathrm{d}^2y}{\mathrm{d}x^2}.

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Other parts of this question

  1. 1(a)(i)b)Find the x-coordinates of the points at which \frac{\mathrm{d}y}{\mathrm{d}x} = 0.[2 marks]
  2. 1(a)(i)c)Find the x-coordinates of the points at which \frac{\mathrm{d}^2y}{\mathrm{d}x^2} = 0.[2 marks]
  3. 1(a)(ii)Hence, determine if the coordinates identified in (i) b) and c) above are at the maxima, minima or points of inflection of y = x^2 e^x.[7 marks]
  4. 1(b)(i)Find the gradient of a tangent to the curve at the point with parameter t.[6 marks]
  5. 1(b)(ii)Find the equation of the tangent at the point where t = \frac{1}{2}.[3 marks]

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