Pay attention to the assumptions of each statement and select all statements that are correct. There may be more than one correct answer. The statements may appear in what seems to be a random order.
The Mean Value Theorem states that for any function f defined on a closed interval [a, b] and differentiable on (a, b) , there exists a number c, with a If the sign of f'(x) changes from to + at a critical point c, then f(c) is a local maximum.
☐ If the sign of f'(x) changes from + to at a critical point c, then f(c) is a local maximum.
If f'(x) > 0 can chance sign at a critical point, but it cannot change sign on the interval between two consecutive critical points as long as the function is defined over the whole interval.
☐ If f'(x) < 0 on an interval then f is decreasing on that interval.
The Mean Value Theorem states that for any function f defined on a closed interval [a, b], there exists a number c, with a ☐ If f'(x) >0 on an interval then f is decreasing on that interval.
If f is differentiable and f'(x) = 0 for all x in (a, b) , then f is constant on (a, b)
