Let f : R → R be given by f ( x ) = ( x – 1)( x – 2)( x – 5). Define F(x)= _ 0 ^ x f(t) d…
Physics · JEE Advanced · NTA Exams — Work, Energy and Power
Let f : R → R be given by f(x) = (x – 1)(x – 2)(x – 5).
Define \(F(x)=\int_{0}^{x} f(t) d t, x>0 .\)Then which of the following options is/are correct?
Define \(F(x)=\int_{0}^{x} f(t) d t, x>0 .\)Then which of the following options is/are correct?
- F has a local maximum at x = 2 .
- F has a local minimum at x = 1 .
- F has two local maxima and one local minimum in (0, ∞).
- F(x) ≠ 0, for all x ∈ (0, 5).
Answer
(C) F has two local maxima and one local minimum in (0, ∞ ).
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