00:01
So we're supposed to use newton's method to find the correct solutions for up to eight decimal places.
00:08
So this is our equation, negative 2x to the 7 minus 5x to the 4th plus 9x cubed plus 5.
00:20
That says look at the graph first to find your initial approximations.
00:24
So, the graph of negative x to a negative, or i'm sorry, an odd number.
00:34
So your evens are going to end up like this.
00:38
Your negative evens are going to look like this.
00:42
Your odds are going to look like this.
00:46
Or your negative odds are going to look like this.
00:50
So we end up having a negative raise to an odd power.
00:57
So it's going to cross, it's going to come down, it's going to go up, and it's going to go down.
01:04
So it's going to cross somewhere between negative 1 and negative 2, and i found this out by just plugging in some values, negative 1 and 0 and between 1 and 2.
01:16
So i'm going to label this a, b, and c, and i'll show you how to find, we're going to assume a1 to be, negative 1 .5, b1 to be negative 0 .5, and c1 to be 1 .5.
01:35
So we're just going to plug one in, and then i'll show you what i got for the answer for the rest of them.
01:42
So we need f prime of x, just equal to negative 14, x to the 6, minus 20 x cubed, plus 27 x squared...