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7-46.
  1. Consider the curve formed by the equation xy2x3y = 12. Homework Help ✎

    1. Show that = .

    2. Find the x-coordinate of each point on the curve where the tangent line is vertical.

Use implicit differentiation.

A tangent line will be vertical where the denominator of the derivative = 0.

Since the denominator has both x and y values, there will be infinitely many ways to make the denominator equal to 0.
But only some (or one) of those ways fit the given curve.