a. Graph the curve r(t) = (t³, t³). Show that r'(0) = 0 and the curve does not have a cusp at t = 0. Explain.

b. Graph the curve r(t) = (t³, t²). Show that r'(0) = 0 and the curve has a cusp at t = 0. Explain.

c. The functions r(t) = (t, t²) and p(t) = (t², t⁴) both satisfy y = x². Explain how the curves they parameterize are different.

d. Consider the curve r(t) = (t^m, tⁿ), where m > 1 and n > 1 are  integers with no common factors. Is it true that the curve has a cusp at t = 0 if one (not both) of m and n is even? Explain.