4. (*) Assume f : [0, 1] - R is continuous with f (0) = f(1). Show that there exists a point c E [0,
4. (*) Assume f : [0, 1] - R is continuous with f (0) = f(1). Show that there exists a point c E [0, 1/2] with f (c) = f(c+ 1/2). Hint: What can you prove about the function g(x) := f(x) - f(x + 1/2)
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