$\"\"$

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The condition are :

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ for all $\"\"$ .

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From the conditions,

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The critical points are at $\"\"$ and $\"\"$ .

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$\"\"$ represents that $\"\"$ is increasing on $\"\"$ .

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$\"\"$ represents that $\"\"$ is decreasing on $\"\"$ .

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At $\"\"$ , $\"\"$ changes from positive to negative, so $\"\"$ has a local maximum at $\"\"$ .

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$\"\"$ represents that $\"\"$ is concave upward on $\"\"$ .

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$\"\"$ represents that $\"\"$ is concave downward on $\"\"$ .

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At $\"\"$ , the concavity changes so the inflection point is at $\"\"$ .

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$\"\"$ represents horizontal asymptote at $\"\"$ .

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$\"\"$ represents that $\"\"$ is an odd function.

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Graph :

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Graph the function such that all the conditions are satisfied :

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$\"\"$

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$\"\"$

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Graph of the function satisfying all the conditions is

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$\"\"$ .