`3cos(x) = x + 1` Use Newton's method to find all roots of the equation correct to six decimal places.
To solve using Newton's method apply the formula,
Plug in f(x) and f'(x) in the formula,
See the attached graph to get the initial values of x.
When f(x)=0 , the values of x are near The curve has three x values x `~~` 0.8 , -1.8 , -3.6
Use these three values for finding the roots of the equation to six decimal places.
Let's solve for the first zero by initial value x_1=0.8
Let's stop iteration as we have same decimal places
Now let's solve for the second zero by initial value x_1=-1.8,
Now let's solve for the third root by initial value x_1=-3.6
Roots of the equation to six decimal places are 0.889470 , -1.862365 , -3.637958