If the function $f(x,y)$ is continuous near the point $(a,b)$, then at least one solution of the differential equation $y' = f(x,y)$ exists on some open interval I containing the point $x = a$ and, moreover, that if in addition the\partial derivative $\frac{\partial f}{\partial y}$ is continuous near $(a,b)$ then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby\guaranteed and, if so, whether uniqueness of that solution is guaranteed.\n$\frac{dy}{dx} = \sqrt{x - y}$; $y(14) = 14$\nSelect the correct choice below and fill in the answer box(es) to complete your choice.\n(Type an ordered pair.)\nA.\nThe theorem implies the existence of at least one solution because $f(x,y)$ is continuous near the point$\boxed{\text{ }}$. This solution is unique because $\frac{\partial f}{\partial y} = \boxed{\text{ }}$ is also continuous near that same point.\nB.\nThe theorem implies the existence of at least one solution because $f(x,y)$ is continuous near the point$\boxed{\text{ }}$. However, this solution is not necessarily unique because $\frac{\partial f}{\partial y} = \boxed{\text{ }}$ is not continuous near that\nsame point.\nC. The theorem does not imply the existence of at least one solution because $f(x,y)$ is not continuous near the point$\boxed{\text{ }}$
