Please help me solve this problem by answering the following questions. Thank you.

For example, you chose f(x) = sin(x)+x²-2x and you chose 0; pi; 2pi; 3pi as nodes.

Start with a non-constant, non-polynomial differentiable function of choice. Choose one that is "easy" to differentiate repeatedly (you will have to take several derivatives.) Choose nodes (x(), f(x()), (x1, f(x1)), (x2, f(x2)), (X3, f(x3) For your function, do the followings: a. Graph the funtion with the approximation on the same axis. b. Graph the difference between the function and the approximation (e. g. let g(x) = f(x) 1(x) and graph that. - n! c. Find the maximal error (Theoretical, using our error formulas; f(n) (n(x))(x-20)... (x_n) the eg stuff with a found for the derivative factor. Idea: use some M that bounds | f(n) (n(x))| on your interval; this is easier with a good choice of function. d. Write a paragraph or two about the the aspects of each approximation (what's good? what's bad? uses?). This should be brief. Start with a non-constant, non-polynomial differentiable function of choice. Choose one that is "easy" to differentiate repeatedly (you will have to take several derivatives.) Choose nodes (x(), f(x()), (x1, f(x1)), (x2, f(x2)), (X3, f(x3) For your function, do the followings: a. Graph the funtion with the approximation on the same axis. b. Graph the difference between the function and the approximation (e. g. let g(x) = f(x) 1(x) and graph that. - n! c. Find the maximal error (Theoretical, using our error formulas; f(n) (n(x))(x-20)... (x_n) the eg stuff with a found for the derivative factor. Idea: use some M that bounds | f(n) (n(x))| on your interval; this is easier with a good choice of function. d. Write a paragraph or two about the the aspects of each approximation (what's good? what's bad? uses?). This should be brief