`x^3 = tan^-1 (x)` Use Newton's method to find all roots of the equation correct to six decimal places.

Expert Answers
gsarora17 eNotes educator| Certified Educator




To solve using Newton's method apply the formula,


Plug in f(x) and f'(x) in the formula


See the attached graph for finding the initial values of x_1.

The curve of the function intersects the x axis at `~~`  0.9 and -0.9 

Let's solve for the first zero x_1=0.9,





Now let's solve for the second zero , x_1=-0.9






So the roots of the equation are 0.902025 and -0.902025

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