Given that the function f (x) = X3 KX is not monotone in the interval (- 3, - 1), then the value range of real number k is______ ． | Math enthusiast | Mathematical art

Given that the function f (x) = X3 KX is not monotone in the interval (- 3, - 1), then the value range of real number k is______ ．

Function derivation f ′ (x) = 3x2-k ∵ is not monotone in the interval (- 3, - 1) ∵ f ′ (x) has zero point in the interval (- 3, - 1) ∵ f ′ (- 3) = 27-k, f ′ (- 1) = 3-K ∵ f ′ (- 3) f ′ (- 1) < 0 ∵ (27-k) (3-K) < 0 ∵ (k-27) (K-3) < 0 ∵ 3 < K < 27, so the answer is: 3 < K < 27

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