The following equation defines a family of plane curves. x3 + y3 - 3axy = c wher

Question

The following equation defines a family of plane curves. x3 + y3 - 3axy = c where c ( - infinity; + infinity). A unique family member passes through every point in the XY-plane except (0. 0) and (a, a). Let (alpha, beta) be a point on one of these plane curves. Your particular parameter and coordinates are a = -8 and (alpha, beta) = (-4,-8). Find the set of ordered pairs (x, y) for which dy/dx is indeterminant. Find the set of ordered pairs (x, y) for which the slope is horizontal. Find the set of ordered pairs (x, y) for which the slope is vertical. Ie Find

Explanation / Answer

the value is different but the method is same: I'm assuming that x^2+1 is all in the denominator, or else 0 wouldn't be in the domain. f(-2) = 2(-2) / [(-2)^2+1] = -4/5 f(-1) = 2(-1) / [(-1)^2+1] = -2/2 = -1 f(0) = 2(0) / [(0)^2+1] = 0/1 = 0 f(1) = 2(1) / [(1)^2+1] = 2/2 = 1 f(2) = 2(2) / [(2)^2+1] = 4/5 So our set of ordered pairs is: {(-2,-4/5), (-1,-1), (0,0), (1,1), (2,4/5)}

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