Newton method for function $f :\mathbb R^n \to\mathbb R$

Question

As stated in the headline: Can I use the Newton method to find the root of a function

$f:\mathbb R^n \to\mathbb R$ ?

The way I know the method this would resolve in sth like this: $x_1 = x_0 + grad(f)^{-1} (x_0)* f(x_0)$

But $grad(f)$ is a vector so how should I take the inverse of that?

Thanks four your help.

Answer 1

So I already found the answer.

It is not possible to use Newton's method for a function $f:R^n -> R$. But the Newtons method can be used to find stationary points of $f$. https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization