Which of the given statements involving extrema are true? If a function f is defined on the interval [a, b], differentiable on (a, b), and decreasing on [a, b], then there must be absolute minimum at b. V Any function f that is defined and continuous on a closed interval [a, b] must have an absolute minimum. If a function f fails to be differentiable at c, then it cannot have a local extreme value at c. Any function f that is defined on an open interval (a, b) must have an absolute maximum. If c is a critical number, then there is a local extreme value at c. Select the true statements involving the mean value theorem and monotonicity. If f' (x) > 0 for all x in an interval, then f is decreasing on that interval. If f is differentiable and f' (x) = 0 for all x E (a, b), then f is constant on [a, b]. If f is continuous on [a, b] and differentiable on (a, b), then there exists at least one e in (a, b) such that f(b) - f(a) = S' (c)(b - a). If f is continuous on [a, b], then there exists at least one c in (a, b) such that f' (c) - Kb)-f() If f' (x)