Apply Rolle’s theorem to find the value of c for the function fx=x3-3x2+2x+2 in the interval [0,1].
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since f(x) is polynomial so it continuous in [0,1] and differentiable in (0,1) .
f(0)=f(1)=2
therefore from rolle s theorem we know that there exists a value 'c' between (0,1) at which tangent is parallel to x axis .
f'(x)= 3x^2-6x+2
f'(c)=0
=3c^2-6c+2=0
c=( 6-2√3)/6
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