Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on the curve where the line tangent to the curve has slope (c) Show that there are no points (x. y) on the curve where the line tangent to the curve is horizontal. (d) Let x and y be functions of time that are related by the equation 1² = 2 + xy. At time t = 5, the dy dt dx dt value of y is 3 and = 6. Find the value of at time 7 = 5.

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