Let $\displaystyle p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3)$ be a cubic polynomial in 1 variable $\displaystyle \lambda$. Use the inverse function theorem to estimate the change in the roots $\displaystyle 0<x_1<x_2<x_3$ if $\displaystyle a=(a_2,a_1,a_0)=(-6,11,-6)$ and $\displaystyle a$ changes by $\displaystyle \Delta a=0.01a$.

How can I use the inverse function theorem to estimate?