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Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2 ....

Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2 . (a) Find dy/dx in terms of t.

(b) Write the equations of the horizontal tangent lines to the curve

(c) Write the equations of the vertical tangent lines to the curve.

(d) Using the results in (a), (b) and (c), sketch the curve for −2 ≤ t ≤ 2.

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