The value of c in the Lagrange’s mean value theorem for the functionfx=x3−4x2+8x+11 , when x∈0,1 is:

fx is a polynomial function                      ∴ It is continuous and differentiable in0,1          Heref0=11,f1=1−4+8+11=16f'x=3x2−8x+8∴f'c=f1−f01−0=16−111=3c2−8c+8⇒3c2−8c+3=0⇒c=8±276=4±73∴c=4−73∈0,1