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3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corres(c) (12 points) Find the exact value of |lf - 2llo to at least 5 decimal places of -P21100 accuracy. Of course, the answer sh

3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2 that you obtained this is true due to the uniqueness of polynomial interpolation!]. Also, verify that P2f(i) for i 0, 1, 2 (b) (10 points) Use the Polynomial Interpolation Error theorem to find an upper bound for the error
(c) (12 points) Find the exact value of |lf - 2llo to at least 5 decimal places of -P21100 accuracy. Of course, the answer should be less than or equal to the upper bound you found in part (b)
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