find all numbers c that satisfy the conclusion of the Mean Value Theorem. f(x) = 3x^2 − 2x + 1  interval= [0, 2]

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The Mean value theorem state that if f(x) in continuous over [a,b] and differentiable over (a,b), then exist a number c, a<c<b, such that 

In our case `f(x)=3x^2-2x+1=>f'(x)=6x-2`

and `f(2)=3*2^2-2*2+1=12-4+1=9`

`f(0)=1`

Hence 

`f'(c)=[9-1]/[2-0]=8/2=4`

`6c-2=4=>6c=6=>c=1`

 

 

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