Consider the equation x2 + y2 = 6y − 10.a. Show that there are no points (x, y) that satis...

Consider the equation x2 + y2 = 6y − 10.

a. Show that there are no points (x, y) that satisfy this equation. [Hint:Complete the square.]

b. Show that by applying implicit differentiation to the given equation, you obtain

The point of this exercise is to show that one must be careful when applying implicit differentiation. Just because it is possible to find a derivative formally by implicit differentiation does not mean that the derivative has any meaning.