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Key data regarding differentiation

Explain whether each statement is true or false. Please give short explanation why and if false, please give an example.

a) The maximum of a function that is continuous on a closed interval can occur at two different values in the interval.

b) If a function is continious on a closed interval, then it must have a minimum on the interval.

c) If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x) + k where k is a constant.

d) If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x-k), where k is a constant.

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