Which two curves are intersected by MC curve at their minimum points:

Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?

The point on the intersection of the tangents drawn to the curve x^2y=1-y at the points where it is intersected by the curve x^2y=1-y at the points where it I intersected by the curve xy=1-y is

Why does MC curve cut the AC curve at its minimum?

Can two isothermal curves intersect each other?

Can two isothermal curves intersect each other?

Can two isothermal curves intersect each other?