Assignment:
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(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) = f(x) + k
(b) g(x) = f(x-k)
(c) g(x) = f(kx)
Provide complete and step by step solution for the question and show calculations and use formulas.