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Q.

Let C be the curve y=x3 (where x takes all real values). The tangent at A meets the curve again at B. if the gradient at B is K times the gradient at A, then |k|  is equal to ________.

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answer is 2.

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Detailed Solution

dydx=3x2=3t2  at A 3t2=T3−t3T−t=T2+Tt+t2 ⇒T2+Tt−2t2=0 ⇒(T−t)(T+2t)=0 ⇒T=t or T=−2t2                           (T=t is not possible)
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