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. 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