Decide if the statement is true or false. give an explanation for your answer. let f(x) = [x], the largest integer less than or equal to x. then f'(x) = 0, so f(x) is constant by the constant function theorem.

a. true. this function satisfies the constant function theorem because f'(x) = 0 everywhere.
b. false. this function does not satisfy the constant function theorem because the derivative f'(x) is not equal to zero everywhere, and the function is not continuous at integral values of x, so f'(x) does not exist there.