If f(x)= _ 0 ^ x e^ t^ 2 (t-2)(t-3) d t for all x ∈ (0, ∞), then
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
If \(f(x)=\int_{0}^{x} e^{t^{2}}(t-2)(t-3) d t\) 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
Answer
(C) there exists some c ∈ (0, ∞ ) such that f ′′ ( c ) = 0
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