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6 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 5(c)(i)

The curve y = px³ + qx² + 3x + 2 passes through the point T(1, 2) and its gradient at T is 7. The line x = 1 cuts the x-axis at M, and the normal to the curve at T cuts the x-axis at N.

Find the values of the constants p and q

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Other parts of this question

  1. 5(a)Find lim (as x→2) (x² + 5x + 6) / (x² - x - 6).[4 marks]
  2. 5(b)(i)Determine f(2)[2 marks]
  3. 5(b)(ii)Determine lim (as x→2⁺) f(x)[2 marks]
  4. 5(b)(iii)Determine lim (as x→2⁻) f(x) in terms of the constant b[2 marks]
  5. 5(b)(iv)Determine the value of b such that f is continuous at x = 2.[4 marks]
  6. 5(c)(ii)Find the equation of the normal to the curve at T[3 marks]
  7. 5(c)(iii)Find the length of MN.[2 marks]

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