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3.7 Numerical methods (A-level only)

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Question 57
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A student is looking for a solution to the equation f(x)=0f(x) = 0f(x)=0. She correctly evaluates:

f(−2)=−1 and f(2)=1 f(-2) = -1 \text{ and } f(2) = 1 f(−2)=−1 and f(2)=1

and concludes that there must be a root in the interval (−2,2)(-2, 2)(−2,2) due to the change of sign. For which of the following functions is this conclusion incorrect?

  • f(x)=12xf(x) = \frac{1}{2}xf(x)=21​x
  • f(x)=2xf(x) = \frac{2}{x}f(x)=x2​
  • f(x)=18x3f(x) = \frac{1}{8}x^3f(x)=81​x3
  • f(x)=xx+4f(x) = \frac{x}{x+4}f(x)=x+4x​
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3.7 Numerical methods (A-level only) Questions

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