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lf $f (x) = x^{3} + 4 x^{2} + λx + 1$ is a monotonically decreasing function of x in the largest possible interval (-2, -2/3). Then

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λ=4

λ=2

λ=-1

λ has no real value

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detailed solution

Correct option is A

Here, f′(x)≤0or 3x2+8x+λ≤0 ∀x∈−2,−23Then situations form f '(x) are as follows: Given that /(*) decreases in the largest possible interval −2,−23.Then f'(x)=0must have roots -2 and -2/3.Thus, product roots =(−2)−23=λ3 or λ=4

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lf f(x)=x3+4x2+λx+1is a monotonically decreasing function of x in the largest possible interval (-2, -2/3). Then

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Ready to Test Your Skills?

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lf $f (x) = x^{3} + 4 x^{2} + λx + 1$ is a monotonically decreasing function of x in the largest possible interval (-2, -2/3). Then