Let f(x)= x x^2 , x>0. Let x_1<x_2<x_3< <x_n< be all the points of local maximum of f and y_1<y_2<y_3< <y_n< be all the points of local minimum of f. Then which of the following options is/are correct?

JEE Advanced 2019 Mathematics question

Let

f(x)=, x>0.

Let be all the points of local maximum of and be all the points of local minimum of . Then which of the following options is/are correct?

Answer: (B),(C),(D)

, which has exactly one root in each interval . As , and decreases, so the first critical point (in , where ) is a minimum: and

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Question ID VK-026956