Let f: R R be given by f(x)=(x-1)(x-2)(x-5). Define F(x)= _0^xf(t) ,dt, x>0. Then which of the following options is/are correct?

JEE Advanced 2019 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2019

Let be given by . Define

F(x)=f(t) dt, x>0.

Then which of the following options is/are correct?

(A) has a local minimum at Correct
(B) has a local maximum at Correct
(C) has two local maxima and one local minimum in
(D) for all Correct

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

Solution

is negative on , positive on , negative on and positive beyond 5. So has local minima at 1 and 5 and a local maximum at 2: (A), (B) true, (C) false (one maximum, two minima).

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Question ID VK-026958