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5 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 1(b)(ii)

On the same pair of axes using a scale of 4 cm for 1 unit on the x-axis and 4 cm for 1 unit on the y-axis, draw the graphs of y = 2^x and y = e^{-x} for -1 \le x \le 3, x \in \mathbb{R}.

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Other parts of this question

  1. 1(a)Solve, for x > 0, the equation 3\log_8 x = 2\log_x 8 - 5.[8 marks]
  2. 1(b)(i)Copy and complete the table for values of 2^x and e^{-x} using a calculator, approximating values to 2 decimal places.[3 marks]
  3. 1(b)(iii)a)Use your graphs to find the value of x satisfying 2^x - e^{-x} = 0.[2 marks]
  4. 1(b)(iii)b)Use your graphs to find the range of values of x for which 2^x - e^{-x} < 0.[2 marks]

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