The first part is the intermediate value theorem.

The second bit is newton Rhapson method.

Newton's Method -- from Wolfram MathWorld

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- May 25th 2009, 11:11 PM #1

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## help!

show that the cubic y=x^3+2x^2+5 has zero somewhere between x=-2.5 and x=-3. pick a suitable starting estimate of the root, x0, and perfrom 3 iterations of newtons method. test your final estimate to see how good it is.

how do i go about this?

thanks

jimmy

- May 26th 2009, 12:56 AM #2
The first part is the intermediate value theorem.

The second bit is newton Rhapson method.

Newton's Method -- from Wolfram MathWorld

- May 26th 2009, 10:28 PM #3

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- May 26th 2009, 10:33 PM #4y=x^3+2x^2+5

(I can't work this out in my head!)

f(x) is continous since it's a polynomial (and all polynomials are continuous).

By the Intermediate Value Theorem f(x) must assume every value between f(-3) and f(-2.5) since it's continuous. Therefore . is a solution to f(x).