00:01
So we're going to use newton's method to find all the solutions of the equation correct to eight decimal places.
00:06
So first we're going to look at the graph.
00:09
So this graph looks something like this.
00:17
Only it actually does hit up here.
00:19
And then when it reaches this cubed root of four, which is roughly about 1 .58, it does not exist after that.
00:27
The reason being is you have 4 minus x cubed equals 0.
00:34
X equals the cubed root of four whenever x equals the cubed root of four then you have the square root of a negative number and we can't have that so we see we have a solution somewhere between zero and negative one and zero and one so we're going to have two solutions so we're going to assume this one is a this one is b and we're going to approximate a1 to equal negative 0 .5 and b and b to equal 0 .5.
01:08
And we'll solve for one, but i'll show you both.
01:12
So first we need to find f prime of x.
01:17
So i broke it down into two different derivatives, and then we're going to, of course, subtract the two.
01:24
So you can see how i did the chain rule for the blue side and the chain rule for the green side...