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?
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?
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.