Newton's Method - How it Can FAIL - More Examples Part 3 of 3

[@NifrasIsmailuoj]

Excellent Explanation Thanks patrickJMT

[@patrickjmt]

my pleasure!

[@terryh728]

Thanks Patrick! Short but ample! Great series

[@Omarakmal10]

Thanks for clearing this up

[@nestoroniFL]

I just watched all 3 of your Newton's Method videos, and I am left with one question. How would you used the formula to approximate the root of a function between two points, rather than just using the first given point? An example would be: find x^3+3x^2-1=0, between the points -4 and 0.

[@lucasm4299]

Use the midpoint between that interval.

[@potong-icecream]

Tutorial question: The velocity flow, v (m/s) of a liquid along a channel satisfies v^3 - 6 v^2 - 348v + 3112 = 0 . Given that there is a root of this equation between v =10 and v = 11, find this root correct three decimal using the Newton Raphson Method (ANS: 10.196m/s) Anyone can help me with this?

[@gremlinextreme101]

@voidzilla It requires the stronger condition of differentiability to even bother considering using Newton's Method

[@mamodibanemasemola3166]

thanks Patrick

[@bkramkoirala]

after 54 iterations x_54=3 i.e. one of the solution, am I right?

[@DanicaMarieMusic]

Thank you!

[@fahadalbasheer4785]

Thank you so much helpful

[@zhiwarsami5737]

Thanks a lot.

[@ICOD73]

You're a life saver

[@kimin8864]

Thank you

[@michaelteach8376]

so what are we trying to find the roots of here?

[@shakyabandara4910]

Thanks

[@lisaakn5796]

is the first guess given in the question??? and if it's not ..how can i find it?

[@socialistguerrilla773]

its a guess , here on purpose its the root of the derivative function so he can illustrate when newtons method doesnt work. But it is just a GUESS , so it shoudnt really matter (as long as its NOT the turning point of the function like here). Usually an initial guess is given in the question for clarity

[@dejanpopovic7903]

Is this the only scenario where Newtons method would fail?

[@Beijing4Life]

I would really go to the college that you are currently teaching at

[@voidzilla]

Don't forget that if f(x) is not continuous Newtons Method will fail.

[@kennedysamarakody4925]

I have a question about this....I am taking Numerical Analysis in college, and my professor gave me this assignment. The function I am dealing with is X^3-X, and to find two more points where the function does not converge to a root.....I found out when the derivative=0, it does not converges....this gives two solution. I found two more values where it does not converges, when N(N(x))=-x....I compose the newton method function with itself and set that equal to -x....this gives me two more numbers where the function does not converge....because geometrically its an infinite loop at N(N(x))=-x. My question here is, how can I find two more roots? My prof told me we can find infinite amount of value where it fails to converge....He told us to find N^4(x), where we compose N(N(x)) with itself and set that equal to -x....I tried doing that, and it gave me a convoluted function...degree 9 so I couldnt solve it. I need help? -thank you in advance.

[@JimmyThePhysicist]

I am sorry dude? I checked this and it worked I got the same solution with newton raphson and the quadratic. I can say that the quadratic formula gave a better answer but the newton method gave me 10 digits same answer!!!!

[@mahdy19959]

Wrong....(x-2)^2 =x^2 +2(x)2 + 2^2