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Tutorial 17 1. The Rolle's Theorem states that if f(x) is differentiable on (a, b) , continuous on (a, b) , and f(a) = f(b) then there is at least one point c in (a, b) where f' ( c ) = 0. If f( x) = x2 - 6x + 5, find the value of c in the interval (1, 5) that satisfies the above theorem. 2. The Rolle's Theorem states that if f(x) is differentiable on (a, b) , continuous on (a, b) , and f(a) = f(b) then there is at least one point c in (a, b) where f' ( c ) = 0. If f(x) = x3 - 4x + 3, find the value of c in the interval (0, 2) that satisfies the above theorem. 3. The Rolle's Theorem states that if f(x) is differentiable on (a, b) , continuous on (a, b) , and f(a) = f(b) then there is at least one point c in (a, b) where f' (c ) = 0. If f( x) = x3 - 7x + 6, find the value of c in the interval (- 3, 2) that satisfies the above theorem