Question: Consider the equation x 2 + y 2 = 6y 10. a. Show that there are no points (x, y) that satisfy this equation.

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

a. Show that there are no points (x, y) that satisfy this equation.

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

dy dx X 3-y

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.

dy dx X 3-y

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