Use the inverse function theorem to estimate the change in the roots

Let be a cubic polynomial in 1 variable . Use the inverse function theorem to estimate the change in the roots if and changes by .

How can I use the inverse function theorem to estimate?

Re: Use the inverse function theorem to estimate the change in the roots

Hey ianchenmu.

If you have a root, then the inverse function would set x = 0 and y = the root. Now if you can find where this happens with the inverse function theorem and do an approximate taylor expansion with a linear component, then you can estimate the changes in the roots.

Re: Use the inverse function theorem to estimate the change in the roots

What means? Can you give me a more complete answer? Thank you.

Re: Use the inverse function theorem to estimate the change in the roots

Quote:

Originally Posted by

**chiro** Hey ianchenmu.

If you have a root, then the inverse function would set x = 0 and y = the root. Now if you can find where this happens with the inverse function theorem and do an approximate taylor expansion with a linear component, then you can estimate the changes in the roots.

What means? Can you give me a more complete answer? Thank you.