Round answer to four decimal places

Question

Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility. (Round your answers to four decimal places.)

f(x) = −x3 + 2.7x2 + 3.55x − 2.422

Newton's method: Graphing utility:

Answer 1

This is an exercise in computation and there is little if any real math involved.

The problem has the solution backwards: first graph the equation to get the approximate roots of which there are 3. Then use the approximate roots to do Newton's Method/

The critical piece of Newton's method is f'(x)=-3x² + 5.4x + 3.55

Remember Newton's Method says: x_n+1 = x_n + f(x_n)/f'(x_n)