Numerical Methods · Interpolation and approximation
The values f(1.0)=2.7183, f(1.1)=3.0042, f(1.2)=3.3201, and f(1.3)=3.6693 are given…
Problem
The values \(f(1.0)=2.7183\), \(f(1.1)=3.0042\), \(f(1.2)=3.3201\), and \(f(1.3)=3.6693\) are given, where \(f\) is \(C^4\) on \([1.0,1.3]\). Approximate \(f'(1.1)\) using (i) the two-point forward difference with \(h=0.10\), (ii) the two-point backward difference with \(h=0.10\), and (iii) the three-point central difference with \(h=0.10\). Report each approximation to four decimal places.
Hint
Forward uses \(1.1\) and \(1.2\); backward uses \(1.0\) and \(1.1\); central uses \(1.0\) and \(1.2\).
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