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Tangents to a Parametric Cubic

• Q(t) = (x(t), y(t)), 0 t 1

• x(t) = axt3 + bxt2 + cxt + dx

• y(t) = ayt3 + byt2 + cyt + dy

• Q'(t) = (d/dt x(t), d/dt y(t))

• x(t) = 3axt2 + 2bxt + cx

• y(t) = 3ayt2 + 2byt + cy

• = the velocity of the object along the path

• Q''(t) = (d/dt x'(t), d/dt y'(t))

• x(t) = 6axt + 2bx

• y(t) = 6ayt + 2by

• = the acceleration of the object along the path

Animation - 10 MAY 95

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