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3 marksDifferentiation

CAPE Integrated Mathematics · 2017 · Paper 2 · Question 5(b)(i)

Differentiate y = (2x + 3)^6 with respect to x.

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  1. 5(a)Given that f(x) = \frac{x^2 - 4}{x + 2}, evaluate \lim_{x \to -2} f(x).[4 marks]
  2. 5(b)(ii)Differentiate y = e^x \sin x with respect to x.[4 marks]
  3. 5(c)Determine the stationary points for the function f(x) = x^3 - 2x^2 + x - 1, stating whether EACH point is a maximum or minimum.[7 marks]
  4. 5(d)If Z(x, y) = x^3 + 4y^2 + \ln y, calculate the partial derivative \frac{\partial Z}{\partial y}.[4 marks]
  5. 5(e)A small business profit function (in dollars) for a year is given by P(x) = 150x - \frac{9}{20}x^2 - 1500, where x represents the number of cakes sold.…[3 marks]

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