If f(x) = _0^x e^ t^2 (t - 2)(t - 3) ,dt for all x (0, ), then

JEE Advanced 2012 Mathematics question

If for all , then

Answer: (A),(B),(C),(D)

, with . on (0, 2), on (2, 3) and on (3, ∞). So f has a local maximum at 2 (A), is decreasing on (2, 3)

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Question ID VK-026119