00:01
Okay, so the root of the equation, f of x, is equal to x to the fourth minus 2x cubed plus 5x squared, can be estimated using newton's method.
00:22
So recall, newton's method says that, well, given the nth approximation, the x sub n plus 1 is equal to, well, x sub n minus f of x of n divided by f prime of x sub n.
00:44
Okay.
00:46
So we have our function f of x, right? so we have to find our derivative.
00:51
So our derivative f prime of x is just equal to, well, 4x cubed minus 6 x squared plus 10x.
01:10
So substituting these values in, we get that x sub n plus 1 plus 1 is.
01:24
Equal to, well, x sub n minus, well, x sub n to the fourth minus 2, x sub n cubed plus 5, x subn squared minus 6 divided by, so we'll use a minus 6 here, right? that's, okay, cut that.
01:58
Divided by 4x sub n cubed minus 6x subn squared plus 10x subn.
02:15
Okay.
02:18
So this, well, becomes, right, we get this as, well, our numerator here becomes 4xx, n to the 4th minus 6x of n cubed plus 10 xx squared minus x a bend plus 2 xubn cubed minus 5x of square plus 6...