Suppose f is a continuous function where f(x)

Suppose $ f $ is a continuous function where $ f(x) > 0 $ for all $ x $, $ f(0) = 4 $, $ f'(x) > 0 $ if $ x < 0 $ or $ x > 2 $, $ f'(x) < 0 $ if $ 0 < x < 2 $, $ f"(-1) = f"(1) = 0 $, $ f"(x) > 0 $ if $ x < -1 $ or $ x > 1 $, $ f"(x) < 0 $ if $ -1 < x < 1 $. (a) Can $ f $ have an absolute maximum? If so, sketch a possible graph of $ f $. If not, explain why? (b) Can $ f $ have an absolute minimum? If so, sketch a possible graph of $ f $. If not, explain why? (c) Sketch a possible graph for $ f $ that does not achieve an absolute minimum.

Suppose $ f $ is a continuous function where $ f(x) > 0 $ for all $ x $, $ f(0) = 4 $, $ f'(x) > 0 $ if $ x < 0 $ or $ x > 2 $, $ f'(x) < 0 $ if $ 0 < x < 2 $, $ f"(-1) = f"(1) = 0 $, $ f"(x) > 0 $ if $ x < -1 $ or $ x > 1 $, $ f"(x) < 0 $ if $ -1 < x < 1 $.
(a) Can $ f $ have an absolute maximum? If so, sketch a possible graph of $ f $. If not, explain why?
(b) Can $ f $ have an absolute minimum? If so, sketch a possible graph of $ f $. If not, explain why?
(c) Sketch a possible graph for $ f $ that does not achieve an absolute minimum.

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