Consider the function $f(x) = |x|$, obviously this function is not differentiable at $x = 0$. But what does that mean for the absolute minimum point? Do I answer the question with simply "the function isn't differentiable at $x = 0$" or do I state that it isn't differentiable but proceed to write the point anyways?
The extrema of functions are found where the derivative is equal to zero OR the derivative is undefined (although those don't necessarily imply extrema exists at those points). This is the second case.
This is pretty clear simply by looking at the graph of the function. To the left and right of (0,0), the function has higher y-values, and also no longer changes slope, as we can see by looking at the derivative. Therefore, the minimum must be (0,0).