$\"\"$

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Derivative of inverse trigonometric functions : $\"\"$ .

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$\"\"$

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$\"\"$

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Again apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a)

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To find the relative extrema, take $\"\"$ .

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$\"\"$

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Equate denominator to zero.

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$\"\"$

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Imaginary values are not considered, there is no relative extrema.

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$\"\"$

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(b)

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To find the inflection points, take $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the function $\"\"$ .

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$\"\"$

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The inflection point is $\"\"$ .

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$\"\"$

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(c)

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To find the Horizontal asymptotes, consider $\"\"$ .

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$\"\"$

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The horizontal asymptote is $\"\"$ .

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To find the Horizontal asymptotes, consider $\"\"$ .

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$\"\"$

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The horizontal asymptote is $\"\"$ .

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Find vertical asymptote.

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Substitute $\"\"$ in the function of $\"\"$ .

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$\"\"$

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There is no vertical asymptotes.

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$\"\"$

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Graph:

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The function is $\"\"$ .

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$\"\"$

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Observe the graph,

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No Relative extrema.

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The inflection point is $\"\"$ .

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The horizontal asymptote is $\"\"$ and $\"\"$ .

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$\"\"$

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No Relative extrema.

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The inflection point is $\"\"$ .

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The horizontal asymptote is $\"\"$ and $\"\"$ .