The implicit equation x^2 + 3 = xy^2 is graphed.   

1. By looking at the graph, how do you expect the slope of the tangent line at the point (1, 2) to compare to the slope of the tangent line at the point (3, 2)?
2. Find dy/dx by using implicit differentiation.
3. Find the exact slopes of the tangent lines at the points (1, 2) and (3, 2).
4. By looking at the graph, between what two consecutive integer x-values do you expect to find that the tangent line is horizontal?
5. Find the exact x-value where the tangent line is horizontal. [Hint: use the substitution y^2 = (x^2+3)/x to help you solve.]

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