Question: consider a plane curve c given by the parametric equations...
Question details
Consider a plane curve C given by the parametric equations x(t) = 6t^{2} and y(t) = 3t^{3} − 4t. Note: In the solution of this problem use symmetry wherever possible.

(a) Find the point A(x0,y0) where C crosses itself. Hint: Solve the system of equations 6t^{2}_{1} = 6t^{2}2 and 3t^{3}_{1} − 4t_{1} = 3t^{3}_{2} − 4t_{2}.

(b) Find equations of both tangents at A.

(c) Find the points on C where tangent is horizontal or vertical.

(d) Determine where C is concave upward or downward.

(e) Indicate by arrows the direction of C.

(f) Find the area enclosed by the loop. Hint: Look at the problem 77 in the section 10.3
of the textbook. Note: If you integrate the loop counterclockwise, the integral will be
negative. Take absolute value of your answer.

(g) Find the arc length of the loop.