Assume fis differentiable and has just one critical point, at x = 3. In parts (a)- (d), you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases. (a) f(1) 3 and f(5)= -3 Ox-3 is a local maximum. Ox= 3 is a local minimum Ox-3 is neither a local maximum nor a local minimum. lim fx) and lim f(x)= Ox-3 is a local maximum. Ox= 3 is a local minimum Ox= 3 is neither a local maximum nor a local minimum. (b) lim (c) f(1) = 2, f(2)= 3, f(4) = 4, and (5) = 5 Ox= 3 is a local maximum. Ox-3 is a local minimum Ox-3 is neither a local maximum nor a local minimum.

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