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Question: the curve c with equation yx3 x2 can be parameterized...

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The curve C with equation y=x^3 +x^2 can be parameterized by r(t)=(x(t),y(t)) = (t^2 -1, t^3 - t), where t is a real parameter.

a) Sketch the curve C (or use a software).

b) control that r(t) is in the curve C for all t.How can you be sure that the parameterization reaches all over C?

c) Control that r'(t) is perpendicular to the gradient \bigtriangledownf(r(t)) where f(x,y)=y^2 -x^3 -x^2.

d) Discuss why the vectors in c) are perpendicular to each other.

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