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1. a) Plot the curve x3 - 4xy + 2y³ = 0 as x varies between -3 and 3 with the aid of the implicitplot command. dy b) Find at all points (x, y) on the curve for which x = 1. dx c) Find the equations of the lines tangent to the curve at the points you found in part b. d) Plot the curve and the tangent lines on the same set of axes. 2. For the following equation y² + y = 2+ P(0,1): a) Plot the equation with the implicit plot command. Check to see that the given point P satisfies the equation. b) Using the implicitdiff command, find a formula for the derivative and find the slope at the given point P. c) Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the equation together with the tangent and the normal lines on a single graph.

Fig: 1