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Given f(x) = 1 x 2 ? 1 , f 0 (x) = ?2x (x...

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Basic Math

Given f(x) = 1 x 2 ? 1 , f 0 (x) = ?2x (x 2 ? 1)2 and f 00(x) =2(3x 2 + 1) (x 2 ? 1)3 . (a) [2 marks] Find the x-intercept and they-intercept of f, if any. (b) [3 marks] Find the horizontal andvertical asymptotes for the graph of y = f(x). (c) [4 marks]Determine the intervals where f is increasing, decreasing, and findthe point(s) of relative extrema, if any. (d) [3 marks] Determinethe intervals where f is concave up, concave down, and find theinflection point(s), if any. (e) [3 marks] Sketch the graph of fand label all important points.

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