Question: Use Theorem 3.9 or Algorithm 3.3 to construct an approximating polynomial for the following data. a. b. c. d. xf(x) 0 1.00000 2.00000 0.5 2.71828

Use Theorem 3.9 or Algorithm 3.3 to construct an approximating polynomial for the following data.
a.

xf(x) 0 1.00000 2.00000 0.5 2.71828 5.43656 f(x) f'(x) -0.25 1.332030.437500 0.25 0.80078-0.625000 f(x) f'(x) 0.10.290049962.8019975 0.2 |-0.56079734 |-2.6159201 0.3 |-0.8 1401972 |-2.9734038 f(x) f'(x) -1 0.86199480 0.15536240 -0.5 0.958020090.23269654 0 1.0986123 0.33333333 0.5 1.2943767 045186776

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