Students were asked to evaluate f'(4) from the following table which shows values of the function f : 1 2 4 6 f(x) 4.2 4.1 4.2 4.5 5.0 5.7 • Student A estimated the derivative as f'(4) × ©)-/ (4) – 0.5, 5-4 Student B estimated the derivative as f'(4)=(4)-J(9) _03. 4-3 • Sudent C suggested that they should split the difference and estimate the average of these two results, that is fS (4)=-(05+0.3)=0.4. (a) Sketch the graph of ƒ, and indicate how the three estimates are represented on the graph. (b) Explain which answer is likely to be the best. (c) Use Student C method to find an algebraic formula to approximate f(x) using increments of size h.

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