InterviewSolution
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InterviewSolution
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What is the interval of f(x) = (x – 1)(x – 2)(x – 3)/(x^3 + 6x^2 + 11x + 6) where f(x) is positive?(a) (-∞, -3) ∪ (3, ∞)(b) (3, -2) ∪ (1, 1) ∪ (2, 3)(c) (-∞, -3) ∪ (2, -1) ∪ (1, 2) ∪ (3, ∞)(d) (-∞, ∞)I got this question in exam.The question is from Sets and their Representations topic in portion Sets of Mathematics – Class 11 |
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Answer» CORRECT CHOICE is (c) (-∞, -3) ∪ (2, -1) ∪ (1, 2) ∪ (3, ∞) To explain: f(x) = (x – 1)(x – 2)(x – 3)/(x^3 + 6x^2 + 11x+ 6) After solving the CUBIC equation (x^3 + 6x^2 + 11x+ 6) we get (x+1)(x+2)(x+3) Now, we can see that this implies f(x) = (x – 1)(x – 2)(x – 3)/(x + 1)(x + 2)(x + 3) So, the critical points of x are, x = 1, 2, 3, -1, -2, -3 So, for f(x) > 0 ᵾ x € (-∞, -3) ∪ (2, -1) ∪ (1, 2) ∪ (3, ∞). |
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