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Video instructions and help with filling out and completing Drawback regulations
Instructions and Help about Drawback regulations
Okay in this video I just want to do a quick little discussion about Newton's method again and how it you know may not work so again that was the Newton's method formula hopefully you've seen the other examples on how to compute things so again this is kind of a basic geometric idea so given the following equation and initial guess we want to know why Newton's method would be bad so suppose we want to find the zeros or the roots to this equation X minus 2 quantity squared minus 1 and we start with the first guess of 2 and again you want to plug in a number that gives you something close to well if we plug 2 into this if we plug 2 into this we'll get well 2 minus 2 we'll get squared minus 1 we'll get negative 1 and and one of the other videos negative 1 was actually you know kind of a would have been our so we started with an initial guess and we got negative 1 out and again that's close to and we started using it and everything worked out great so what's the issue why would x equals 2 be bad here so I'm just gonna graph this function real quick remember x squared is a parabola X minus 2 on the inside actually shifts it two to the right okay so there's x equals two and then the minus 1 would move it down 1 unit so that would be the vertex of our parabola and it's gonna cross the you know it's gonna cross the x axis somewhere I think we can almost maybe you can almost figure out the answers here but suppose again you know just talking about geometrically why you can go wrong what Newton's method does is somehow when you start at your first guess what it does is it looks at a tangent line at that point and the tangent line you know hopefully you pick a point where the tangent line will eventually hit the x-axis because if that tangent line hits the x-axis actually that place where it hits so suppose instead of using two we use some other value maybe like two point six so 2.6 I'm gonna get a tangent line that looks something like that so if 2.6 if that was my first guess this x-intercept Newton's method that's what it actually does it picks out the x-intercept so whatever this x-intercept is when we go through Newton's method and we do this iteration and compute our formula for a little X sub 2 X sub 2 is magically gonna be that point and then the idea is well maybe I could go up here and find that point on the graph and I could find a new tangent line and again we're trying to get close to X intercepts on the real graph so notice by looking at this new.