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3- Name the two religious centers as the second urbanisation |
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Answer» We have`f(x) = x^4/4 - x^3 - 5x^2 + 24X + 12``=> f'(x) = x^3 -3x^2 - 10x + 24`As x = 2 satisfies the above equation. Therefore, (x − 2) is a factor.On PERFORMING long division`(x^3 - 3x^2- 10x + 24)/(x -2) = x^2 -x -12 = (x + 3)(x+4)` `=> f'(x) = (x - 2) (x + 3) (x -4)`Here, the critical points are 2, −3, and 4.The possible intervals are (−∞, −3), (−3, 2), (2, 4), (4, ∞)a) For f(x) to be STRICTLY increasing, we MUST havef'(x) > 0`=> (x - 2)(x + 3) (x - 4) > 0``=> x in (-3,2) U (4,oo)`So, f(x) is strictly increasing on x∈(−3, 2) ∪ (4, ∞). |
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