Problem 34E

34. (a) The curve with equation $y^{2}=x^{3}+3 x^{2}$ is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point $(1,-2)$.

(b) At what points does this curve have horizontal tangents?

(c) Illustrate parts (a) and (b) by graphing the curve and the tangent lines on a common screen.

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