Let f be continuous on [1,5] and differentiable on (1,5) except possibly at x=4, where f′(4) does not exist. Suppose f′(2)=0. Which of the following must be true about f on [1,5]?
a) f attains its absolute maximum at x=2 because f′(2)=0.
b) f attains both a local maximum and a local minimum at x=4 because f′(4) does not exist.
c) At least one absolute extremum occurs at x=1, x=4, \text{or}\, x=5.
d) No information about absolute extrema can be determined from the given data.