The value of the function f(x) is known at three points 𝑓(0) = 1, 𝑓(1) = 2 , 𝑓(3) = −1. (a) Writ

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The value of the function f(x) is known at three points
𝑓(0) = 1, 𝑓(1) = 2 , 𝑓(3) = −1.
(a) Write down the first three terms of the Taylor series 𝑓(𝑥) about 𝑥 = 1.
(b) Use the Taylor series from part (a) to express 𝑓(0) and 𝑓(3).
(c) Determine 𝑓′(1) and the second derivatives 𝑓′′(1).

The Value Of The Function F X Is Known At Three Points F 0 1 F 1 2 F 3 1 A Write Down The First Three T 1 (11.9 KiB) Viewed 34 times

• 4. (1+4+2-7 marks) The value of the function f(x) is known at three points f(0) = 1,f(1) = 2,f(3) = -1. (a) Write down the first three terms of the Taylor series f(x) about x = 1. (b) Use the Taylor series from part (a) to express (0) and (3). (c) Determine f'(1) and the second derivatives f"(1).