If f (x) = (x-1) (X-2) (x-3) (x-4), how many real roots does the derivative of the equation have? If f (x) = (x-1) (X-2) (x-3) (x-4), how many real roots does the derivative of the equation have I don't know how to determine the image between 1 and 2, 2 and 3, 3 and 4. I feel that there is at least one between them, not one

F (x) = (x-1) (X-2) (x-3) (x-4) f (1) = 0; f (2) = 0; f (3) = 0; f (4) = 0  in (1,2), there must be a ξ 1 such that f '(ξ 1) = 0 in (2,3), there must be a ξ 2 such that f' (ξ 2) = 0 in (3,4), there must be a ξ 3 such that f '(ξ 3) = 0 in (3,4)

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