Find all numbers c that satisfy the conclusion of Rolle's Theorem.

*f*(*x*) = *x^3 *− *x^2* − 2*x* + 8 interval= [0, 2]

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`f(0)=8`

`f(2)=8-4-4+8=8`

f is continuous, and differentiable on [0,2].

therefore by Rolle's Theorem, `EEc in(0,2) | f'(c)=0`

Let's find c.

`f'(x)=3x^2-2x-2`

using the quadratic formula `f'(x)=0` iff `x=(2+-sqrt(4+4*3*2))/(6)`

`x=(1+-sqrt(7))/3`

**Since** `c in(0,2)` , `c=(1+sqrt(7))/3`

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