I do not understand most comments here.
Gradient descent is just the same as the tangent method. It is ubiquitously used, e.g. find minimum of whatever polynomial of degree >= 4.
Calculating derivative and finding 0 of the derivative is still the same problem. You look for a numerical solution using gradient descents. Bisection is slower and not so effective for multivariate functions.
I would say the opposite: there are more optimisation problems where gradient descent is used than not (excluding everything which can be solved by linear systems)
I think it's a hopeless problem. Maybe someone as third part confirmation to the business manager about the complexity of the task