(558, #21) Graph the curve in a viewing rectangle that displays all the important aspects of the curve.

Solution:

Since

x'(t) = (4 t^3 -6 t^2 -4t) = 2t(2t^2 -3t -2)= 2t(t-2)(2t+1)

x changes direction at t = -1/2, 0, and 2.

Since


y changes direction at .

So we graph on the interval [-1.4, 2.4], an interval large enough to show all the points where the curve changes direction.

Maple Code

by: nl