multiplicity

Concept

If $f(x^{\ast })=f^{\prime }(x^{\ast })=f^{\prime \prime }(x^{\ast })=\cdots =f^{(m-1)}(x^{\ast })=0$ and $f^{(m)}(x^{\ast })\ne 0$, we can say $x^{\ast }$ is a solution with multiplicity of $m$.

Example

$y=(x-1{)}^3$ indicated $1$ is a root/solution with multiplicity of 3