4. Consider the parameterised plane curve known as Tschirnhausen's cubic: r(t) = (1 3t2, t(3- t2)),...

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4. Consider the parameterised plane curve known as Tschirnhausen's cubic: r(t) = (1 3t2, t(3- t2)), for t R. (a) Show that the curve has a self-intersection at the point (-8,0) (b) Compute the curvature of this plane curve. Then, identify the location of maximu curvature and plot this point on a sketch of the plane curve. + find 4. Consider the parameterised plane curve known as Tschirnhausen's cubic: r(t) = (1 3t2, t(3- t2)), for t R. (a) Show that the curve has a self-intersection at the point (-8,0) (b) Compute the curvature of this plane curve. Then, identify the location of maximu curvature and plot this point on a sketch of the plane curve. + find