GarySanchez
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- Joined
- Nov 7, 2010
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I've been doing optimization problems all day and I just can't use my brain anymore. Can you help me figure this out and why it is what it is?
Which, if any, of the first four statements is false? If you think that all are true, answer with the fifth statement.
A) If g'(x) > 0 for x < b, g'(x) < 0 for b < x, and g(x) is continuous at x = b, then [b, g(b)] is a local maximum for y = g(x).
B) If g'(x) exists at x = b, then g(x) is continuous at x = b
C) If g''(x) exists at x = b, then g'(x) is continuous at x = b
D) If [b, g(b)] is a local maximum for y = g(x),then g'(b) must be 0
E) All of the above are true
Which, if any, of the first four statements is false? If you think that all are true, answer with the fifth statement.
A) If g'(x) > 0 for x < b, g'(x) < 0 for b < x, and g(x) is continuous at x = b, then [b, g(b)] is a local maximum for y = g(x).
B) If g'(x) exists at x = b, then g(x) is continuous at x = b
C) If g''(x) exists at x = b, then g'(x) is continuous at x = b
D) If [b, g(b)] is a local maximum for y = g(x),then g'(b) must be 0
E) All of the above are true