00:01
Here we want to use both newton's method and the second method to calculate the root for the linear equation x to the third plus two times x plus 4 equals 0.
00:17
And we are going to use as initial guess for the newton's method, x not equals 0.
00:26
And beside this one, we are going to use as the other guess for the second method, the first guess from newton's method.
00:35
So we got to apply first the nugent's method to obtain his first guess and use that value besides the value zero as the first two guesses for the second methods.
00:50
And we identify here the function f is equal to f f of x equal to x to the third plus two times x plus four.
01:07
So with derivative that is using the newton's method is equal to three times x square plus two we know that the newton's method is read as x of n plus 1 equals x of n minus f at x of n divided by derivative of f at x of n for n greater than or equal 0 and the initial guess x not is given and here we use both f and its derivative given by these expressions here and for the second method we have the expression x of n equals x of n minus 1 minus f at x of n minus 1 times a fraction in the numerator it has x of n minus 1 minus 2 divided by f at x of n minus 1 minus 1 minus 1 minus 2 divided by f at x of n minus 1 minus 1 minus f at x event minus 2 and that for n greater than equal to 2 because we start by calculating x2 from x0 and x1 which are given so these are the expression in the second method we only use the function f and in the newton's method we use both the function f and its derivative given by these two expressions here so we're going to start using or applying the newton's method for the initial guess x not equals 0.
02:57
If we do that, we're going to have for the newton's method, then x not equals 0.
03:11
And from that, we calculate the following iterates x1 approximately equal to...