Consider the function f(x) = x-3x + 3. (a) Use a graphing calculator to graph f....

 

 

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Consider the function f(x) = x-3x + 3. (a) Use a graphing calculator to graph f. (b) Use Newton's method with xo (c) Repeat part (b) using x0 = 1 = 1 as an initial guess. as an initial guess and observe that the result is different. (#4)). (d) To understand why the results in parts (b) and (c) are different, sketch the tangent lines to the graph of f at the points (1, f(1)) and . Find the x-intercept of each tangent line and compare the intercepts with the first iteration of Newton's method using the respective initial guesses. (e) Write a short paragraph summarizing how Newton's method works. Use the results of this exercise to describe why it is important to select the initial guess carefully. Consider the function f(x) = x-3x + 3. (a) Use a graphing calculator to graph f. (b) Use Newton's method with xo (c) Repeat part (b) using x0 = 1 = 1 as an initial guess. as an initial guess and observe that the result is different. (#4)). (d) To understand why the results in parts (b) and (c) are different, sketch the tangent lines to the graph of f at the points (1, f(1)) and . Find the x-intercept of each tangent line and compare the intercepts with the first iteration of Newton's method using the respective initial guesses. (e) Write a short paragraph summarizing how Newton's method works. Use the results of this exercise to describe why it is important to select the initial guess carefully.