An object of mass 2 kg is placed at rest on  a frictionless horizontal surface.  A horizontal force is given by F¯  =    (x2−9)ℓ∧ N  acts on it along x-axis.  Kinetic energy of the object will be maximum at

from work energy theorem work done = change in KE d(KE)=dW= F.dx ⇒KE=∫ F.dx KE =    ∫(x2−9) dx  =   x33−9x to find KE is maximum or minimum , ddxKE=0 ⇒(x2−9)=0 ⇒x=±3 case 1: if x =+3 →d2dx2KE=ddx(x2−9)=2x=2(3)=+6 is positive⇒minimum case 2: if x =-3 →d2dx2KE=2(-3)=-6 is negative⇒maximum ∴KE is maximum at x=-3m