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If the tangent to the curve

Question:

If the tangent to the curve, $y=x^{3}+a x-b$ at the point $(1,-5)$ is perpendicular to the line, $-x+y+4=0$, then which one of the following points lies on the curve ?

  1. $(-2,2)$

  2. $(2,-2)$

  3. $(2,-1)$

  4. $(-2,1)$


Correct Option: , 2

Solution:

 

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