Question 4 - A-Level Maths

Exam Board	OCR MEI
Module	Further Numerical Methods (Further Numerical Methods)
Session	Specimen
Topic	Sign Change & Interval Methods
Type	Numerical Differentiation Estimates

4 The table below gives values of a function \(y = \mathrm { f } ( x )\).

\(x\)	0.2	0.3	0.35	0.4	0.45	0.5	0.6
\(\mathrm { f } ( x )\)	0.789922	0.754628	0.749199	0.749997	0.756257	0.767523	0.804299

Calculate three estimates of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(x = 0.4\) using the central difference method.
State the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(x = 0.4\) to an appropriate degree of accuracy. Justify your answer.