Mathematics

Problem

The trajectory of a point in the plane is given by

x=3t-t^{3}

and

y=3t^{2}+1

for

-2\le t\le 2

. a. (i) Determine all real values of

t

in the given interval for which the tangent to the curve is vertical. b. (ii) Find the corresponding coordinate points on the curve. c. (iii) State how many distinct vertical tangents the curve possesses in the stated interval.

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