$\"\"$

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The parabola equation is $\"\"$ and the point is $\"\"$ .

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Find the curvature.

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Apply the curvature formula from 69(b): $\"\"$ .

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$\"\"$

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

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

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The curvature is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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The curvature is $\"\"$ .

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$\"\"$

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(b)

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Find the at what point the curvature is maximum.

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The curvature is $\"\"$ .

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The curvature is maximum when $\"\"$ is minimum.

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$\"\"$ is minimum when $\"\"$ .

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

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$\"\"$ .

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The curvature is maximum at point $\"\"$ .

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$\"\"$

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(a) The curvature at point $\"\"$ is $\"\"$ .

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(b) The curvature is maximum at point $\"\"$ .