Question 1 using matlab

interval, similar to Figure 3.5 (a) 15 base points (b) 25 base points I3) P(.3)1 that would result if two additional interpolation points (x, )(, 1) and ( 17.m = (.5. f(.5)) are added. What assumptions have you made to produce this estimate? Problems 1. (a) Use the method of divided differences to find the degree 4 interpolating polynomial P4x) for the data (0.6, 1.433329), (0.7,1.632316). (0.8,1.896481), (0.9,2.247908), and 1.0,2.718282). (b) Calculate P4(0.82) and P4(0.98). (c) The preceding data come from the function f(x) = e'. Use the interpolation error formula to find upper bounds for the error at x = 0.82 and x = 0.98, and compare the bounds with the actual error. (d) Plot the actual interpolation error P(x)- eon the intervals [.5, 1] and [0, 2] 2. Plot the interpolation error of the sin! key from Program 3.3 on the interval [-27,2 3. The total world oil production in millions of barrels per day is shown in the table that follows. Determine and plot the degree 9 polynomial through the data. Use it to estimate 2010 oil production. Does the Runge phenomenon occur in this example? In your opinion, is the interpolating polynomial a good model of the data? Explain