Find the points of maximum and absolute minimum of the following function of two variables $$f(x,y)=\frac{\cosh (x-y)}{x}\left(e^{x}-x-1\right)$$ on the set: $$M=\left\{(x,y)\in \mathbb R^2 \ \Bigl|\ x+y\leq L\right\}$$ Let us initially extreme points internal to M, ie $$int(M)=\left\{(x,y)\in \mathbb R^2 \ \Bigl|\ x+y< L\right\}$$ and is simple to verify that $(0,0)$ is a saddle point.
For the extreme point in the boundary of M: $$\partial M=\left\{(x,y)\in \mathbb R^2 \ \Bigl|\ x+y = L\right\}$$ we apply the Lagrange multiplier method. Is correct the procedure?
Now I get some equations that (in my opinion) are impossible to solve in closed form. Or not?
What do you think?
