$\"\"$

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The magnitude of the force is $\"\"$ .

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Where $\"\"$ is the positive constant called the coefficients of friction.

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$\"\"$ is the weight of an object.

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Find the critical points.

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Differentiate the force $\"\"$ with respect to $\"\"$ , holding $\"\"$ and $\"\"$ as constants.

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$\"\"$

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To find the critical points, equate its derivative to zero.

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$\"\"$

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$\"\"$

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Find the value of $\"\"$ at the end points.

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

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$\"\"$

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

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$\"\"$

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Find the value of $\"\"$ at the critical number.

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Substitute $\"\"$ in the function.

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$\"\"$

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Now $\"\"$ then $\"\"$ .

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$\"\"$ .

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Observe the values.

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$\"\"$ , hence $\"\"$ is minimized then $\"\"$ .

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$\"\"$

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When $\"\"$ is minimized then $\"\"$ .