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The curve is $\"\"$ and inflection point is $\"\"$ .

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Inflection point is a point of the curve where the curve changes from up to down or down to up.

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Substitute $\"\"$ in the curve equation.

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$\"\"$

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Rewrite the curve.

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$\"\"$

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

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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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Find the values of $\"\"$ and $\"\"$ .

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Inflection point is $\"\"$ .

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Equate $\"\"$ to zero and substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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Substitute $\"\"$ in equation (1).

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$\"\"$

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Substitute $\"\"$ in equation (1).

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$\"\"$

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Find the additional inflection points.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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No inflection point is obtained, so $\"\"$ and $\"\"$ are not consider.

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Now substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Find the inflection points.

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Equate $\"\"$ to zero.

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$\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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Therefore the inflection points at $\"\"$ . $\"\"$ and $\"\"$ .

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The curve is $\"\"$

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Substitute $\"\"$ and $\"\"$ in the above curve.

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$\"\"$

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The obtained curve is $\"\"$ .

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Substitute $\"\"$ in the above curve.

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$\"\"$

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Substitute $\"\"$ in the above curve.

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$\"\"$

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Substitute $\"\"$ in the above curve.

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$\"\"$

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The inflection points are $\"\"$ , $\"\"$ and $\"\"$ .

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Therefore the additional inflection points are $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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The additional inflection points are $\"\"$ and $\"\"$ .