007A Sample Final 2, Problem 10

Let

$f(x)={\frac {4x}{x^{2}+1}}$

(a) Find all local maximum and local minimum values of  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f,}   find all intervals where  $f$  is increasing and all intervals where  $f$  is decreasing.

(b) Find all inflection points of the function  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f,}   find all intervals where the function  $f$  is concave upward and all intervals where  $f$  is concave downward.

(c) Find all horizontal asymptotes of the graph  $y=f(x).$

(d) Sketch the graph of  $y=f(x).$

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Solution

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