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Since f(x)=(x-1)^(10) is polynomial function, and we know that polynomal function is continuwus and differentiahle on R.:.f(x)=(x-1)^(10) is continuous on [0,2] and differentiable on (0,2)By Mean Value Theirem EE c in(a,b) s.t{:[f^(')(c)=(f(b)-f(a)quad b-a)/(b-a)","b=2],[f^(')(x)=10(x-1)^(49)quad{(dx^(n))/(dx)=nx^(n-1)}],[10(x-1)^(9)=(f(2)-f(0))/(2-0)],[10(c-1)^(9)=(1-1)/(2)=0],[10(c-1)^(9)=0 ... See the full answer