Find the y-value for x 096 by substituting x 096 in the

Question

(a) If x³ + y³ - xy² = 5, find dy/dx.

(b) Using your answer to part (a), make a table of approximate y-values of points on the curve near x =

1, y = 2. Include x = 0.96, 0.98, 1, 1.02, 1.04.

(c) Find the y-value for x = 0.96 by substituting x = 0.96 in the original equation and solving for y using a computer or calculator. Compare with your answer in part (b).

(d) Find all points where the tangent line is horizontal or vertical.