OCR MEI Further Numerical Methods 2021 November — Question 4

Exam BoardOCR MEI
ModuleFurther Numerical Methods (Further Numerical Methods)
Year2021
SessionNovember
TopicSign Change & Interval Methods
TypeNumerical Differentiation Estimates
4 The table shows some values of \(x\) and the associated values of \(\mathrm { f } ( x )\).
\(x\)44.00014.0014.014.1
\(\mathrm { f } ( x )\)44.00023864.00238714.02394684.2472072
  1. Calculate four estimates of the derivative of \(\mathrm { f } ( x )\) at \(x = 4\).
  2. Without doing any further calculation, state the value of \(f ^ { \prime } ( 4 )\) as accurately as you can, justifying the precision quoted.
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