I'm having trouble determining a function that looks like this in $[-1,1]$.
Basically, the requirements are that:
- It passes through the origin
- When $x$ is positive, it has a tiny negative slope. Basically needs to hug the x-axis
- When $x$ is negative, it has huge negative slope, basically needs to hug the y-axis
- $x$ must exist from $-1$ to $1$. Doesn't matter what happens beyond those points
- Function must be differentiable from $-1$ to $1$.
- Can be some crazy polynomial if needed.
- The point $(0,0)$ must be as close to a corner as possible but still differentiable.
Thanks!