If the tangent drawn to the curve y = x ^3 at a point ( , ) cuts again the curve at another point ( ₁, ₁ ) , then ₁ =

Step-by-step solution

y=x^3 Equation of tangent line at point ( , ) is: (y- )=3 ^2(x- ) ( ₁, ₁ ) lies on equation (i), we get ₁- =3 ^2 ( ₁- ) array r ₁^3- ^3=3 ^2 ( ₁- ) ( ₁, ₁ ) &( , ) lies on y=x^3 array ₁^3 ^3 -1=3 ( ₁ -1 ) ( ₁ )^3-3 ₁ +2=0 Let y= ₁ Then, y^3-3 y+2=0 (y-1)^2(y+2)=0 aligned & ( ₁ -1 )^2 ( ₁ +2 )=0 & ₁ -1=0 or ₁ =2 & ₁= (not possible) or ₁ =-2 & ( ₁ )^3=-8 aligned Now, ₁ = ₁^3 ^3 = ( ₁ )^3=-8