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Most people's first reaction to this question is exactly the same as Ruth's:
"My initial conjecture was that the minimum value of f(x) is when x=0 for any value of a, because the function is even and increases as |x| increases."Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.