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AP® Calculus AB-BC

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Difficult

Tangent at Point of Inflection

APCALC-BXNMMH

Find the equation of the line tangent to the parametric curve $x( t ) =2t-1,\quad y( t ) ={ t }^{ 3 }-{ 3t }^{ 2 }+1$ at its point of inflection.

A

$y=-\cfrac{3}{2}x+\cfrac{5}{2}$

B

$y=-\cfrac{3}{2}x+\cfrac{1}{2}$

C

$y=-\cfrac{3}{2}x-\cfrac{1}{2}$

D

$y=\cfrac{3}{2}x-\cfrac{5}{2}$