My understanding is that the objective function must have a maximum and a minimum under this constraint condition, and the objective function is derivable. If both the maximum and the minimum are in it, there will be at least two suspicious extreme points, but only one can be found, that is to say, there is a place where the maximum value is taken, which is not derivable, so the only derivable and non-derivable point is the endpoint. So the minimum value must exist at the endpoint. If you don't understand, we can discuss it again.