$\"\"$

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The function is $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Critical points of the function are the points where the first derivative is equals to zero.

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Consider $\"\"$ .

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Newton $\"\"$ s approximation method formula: $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Perform newton approximation for $\"\"$ .

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$\"\"$

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$\"\"$ .

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Perform newton approximation for $\"\"$ .

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$\"\"$

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$\"\"$ .

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Since the two approximations differ by less than $\"\"$ .

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Therefore, critical point is $\"\"$ .

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Graph:

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$\"\"$

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Observe the above graph:

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The critical point number is at $\"\"$ .

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The relative extrema is $\"\"$ .

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$\"\"$

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Graph of the function $\"\"$ :

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$\"\"$

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The critical point number is at $\"\"$ .

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The relative extrema is $\"\"$ .