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Question

Let S be the set of real values of parameter λ  for which the equation f(x) = 2x3  3(2+λ)x2 + 12λ x has exactly one local maximum and exactly one local minimum. Then S is a subset of
  1. None of these
  2. (-4, ∞) 
  3. (-3, 3) 
  4. (3, ∞) 


Solution

The correct option is D (3, ∞) 
f(x) = 2x3  3(2+λ)x2 + 12λ x f(x) = 6x2  6(2+λ)x + 12λf(x) = 0  x = 2, λ
If f(x) has exactly one local maximum and exactly one local minimum, then λ  2.

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