Function and Solution Approximation Consider the function f(x)=πx. a. Construct the first three Taylor polynomials of f centered at a=0. b. Use your Taylor polynomials to estimate π,1/π, and π
​. c. Construct graphs of your Taylor polynomials and the original function f(x) in the same window in Desmos. Which polynomial seems to best estimate f(x) ? d. Consider the equation πx=xπ. Estimate its solution by completing the following: a. Represent the equation as the problem g(x)=0 and state the function g(x). b. Use the Intermediate Value Theorem to find a closed interval where a solution exists. c. Using your closed interval from part (b), choose an initial approximation x1​ to the true solution. Then use Newton's Method to approximate the true solution to within six decimal places. (hint: you are strongly encouraged to set up a function in Desmos that will calculate the Newton's Method formula for you)