If f (x) = \int^{x}_{0} e^{t^2} (t-2)(t-3) dt for all x ∊ (0 , ∞), then [JEE Adv 2012 P2]

f has a local maximum at x = 2.

there exists some c ∈ (0, ∞) such that f ′′(c) = 0.

f has a local minimum at x = 3.

Application of Derivatives

Section: Mathematics

Question : 22 of 32

Marks: +1, -0

If f (x) =

∫

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

[JEE Adv 2012 P2]

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