If f(x) = x^3 + 4x^2 + x + 1 is a monotonically decreasing function of x in the largest possible interval (-2, -2/3) then

JEE Advanced Mathematics question

If is a monotonically decreasing function of in the largest possible interval then

Answer: (A)

. is decreasing where , i.e. between the roots of . For this largest interval to be exactly , the roots must be and .

Sum of roots:

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Question ID VK-109421