Given the case we have a multivariable function $f(x,y,z)$ and a hypercuboid defined by its intervals $[x_l,x_u], [y_l, y_u], [z_l, z_u], [w_l, w_u]$ where $f(x,y,z) = w$.
How can we check if $f$ intersects with a hypercuboid? I'm not looking here for an explicit example for the beginning, but more on the general idea how to approach such a problem :)
Edit/Update:
Assume that our function would be e.g. the following:
$f(x,y,z) = x*sin(c*y+z)$.
This function is periodic and continuous. Computing the extreme points would be achieved by computing the Hessian. But how can we compute the min and max within given intervals like in our example?
Thank you in advance for any hints, Dan