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If the absolute maximum value of the function \(f(x) = (x^2 – 2x + 7) \,e^{(4x^3 - 12x^2 - 180x + 31)}\) in the interval [–3, 0] is f(α), then : (A) α = 0 (B) α = –3(C) α ∈ (–1,0)(D) α ∈ (–3,–1) |
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Answer» Correct option is (B) α = –3 \(f'(x) = e^{(4x^3 - 12x^2 - 180x + 31)}(12(x^2 - 2x + 7)(x + 3)(x - 5)+ 2(x - 1))\) for x ∈ [–3,0] ⇒ f’(x) < 0 f(x) is decreasing function on [–3,0] The absolute maximum value of the function f(x) is at x = –3 ⇒ α = –3 |
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