Let be continuous on [a, b] and differentiable on (a, b). Also, suppose that (a) =
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Let ƒ be continuous on [a, b] and differentiable on (a, b). Also, suppose that ƒ(a) = ƒ(b) and that c is a real number in the interval such that ƒ'(c) = 0. Find an interval for the function g over which Rolle's Theorem can be applied, and find the corresponding critical number of g (k is a constant).
(a) g(x) = ƒ(x) + k
(b) g(x) = ƒ(x - k)
(c) g(x) = ƒ(kx)
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