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IIT JEE Advanced 2012 Paper 2

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Question : 60

Total: 60

If f (x) =

et2(t−2)(t−3)dt for all x ∊ (0 , ∞), then

f has a local maximum at x = 2.
f is decreasing on (2, 3).
there exists some c ∈ (0, ∞) such that f ′′(c) = 0.
f has a local minimum at x = 3.

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