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

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