Use implicit differentiation to calculate higher derivatives.

Use the method of the previous exercise to compute y" at the point (1, 1) on the curve x³ + y³ = 3x + y − 2.

Data From Exercise 61

Calculate y" at the point (1, 1) on the curve xy² + y − 2 = 0 by the following steps:
(a) Find y' by implicit differentiation and calculate y' at the point (1, 1).
(b) Differentiate the expression for y' found in (a). Then compute y" at (1, 1) by substituting x = 1, y = 1, and the value of y' found in (a).