- #1
jostpuur
- 2,116
- 19
Assume that [itex]f:\mathbb{R}^N\to\mathbb{R}[/itex] is a differentiable function and that [itex]x_0\in\mathbb{R}^N[/itex] is a local minimum of [itex]f[/itex]. Also assume that [itex]N\geq 2[/itex] and that the gradient of [itex]f[/itex] has no other zeros than the [itex]x_0[/itex]. In other words
[tex]
\nabla f(x)=0\quad\implies\quad x=x_0
[/tex]
Is the [itex]x_0[/itex] a global minimum?
[tex]
\nabla f(x)=0\quad\implies\quad x=x_0
[/tex]
Is the [itex]x_0[/itex] a global minimum?