JEE Advanced Mathematics question

Mathematics Application of Derivatives JEE Advanced

is a polynomial of the third degree which has a local maximum at . If , and has a local minimum at then

(A)
(B) has a local minimum at Correct
(C) is increasing in Correct
(D)the distance between and , where is a point of local minimum, is

Answer: (B),(C)

Solution

Let . Then: - has an extremum at : . - : . - : . - : .

Subtracting the last two: , so

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Question ID VK-110620