Question: the curve c with equation yx3 x2 can be parameterized...
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 f(r(t)) where f(x,y)=y^2 -x^3 -x^2.
d) Discuss why the vectors in c) are perpendicular to each other.