Maxima and MinimaMedium
Question
Let S be the set of real values of parameter λ for which the function f(x) = 2x3 - 3(2 + λ)x2 + 12λx has exactly one local maxima and exactly one local minima. Then the subset of S is -
Options
A.(5, ∞)
B.(-4, 4)
C.(3, 8)
D.(-∞ , -1)
Solution
f (x) = 2x3 - 3(2 + l)x2 + 12λx
f′(x) = 6x2 - 6(2 + λ)x +12λ
D > 0
36(2 + λ)2 - 24.12.λ > 0
⇒ (λ - 2)2 > 0
⇒ λ ≠ 2
so required set is option (A, C, D)
f′(x) = 6x2 - 6(2 + λ)x +12λ
D > 0
36(2 + λ)2 - 24.12.λ > 0
⇒ (λ - 2)2 > 0
⇒ λ ≠ 2
so required set is option (A, C, D)
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