$\"\"$

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The function is $\"\"$

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(a)

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Find the polynomial of the function $\"\"$ of degree $\"\"$ .

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Consider the fifth polynomial of the function is $\"\"$ .

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The curvature of the line is $\"\"$ .

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The curvature of the straight line is zero.

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Hence the curvature of the straight line $\"\"$ must be zero at $\"\"$ and $\"\"$ .

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The value of $\"\"$ and $\"\"$ .

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The slope of the straight line zero, hence $\"\"$ and $\"\"$ .

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Since the function $\"\"$ is continuous, hence $\"\"$ and $\"\"$ .

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$\"\"$

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The fucntion is $\"\"$ .

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Since $\"\"$ , then $\"\"$ .

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Since $\"\"$ , then $\"\"$ .

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Since $\"\"$ , then $\"\"$ .

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Since $\"\"$ , then $\"\"$ .

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Since $\"\"$ , then $\"\"$ .

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Rewrite $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Apply derivative on each side.

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Since $\"\"$ , $\"\"$ .

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

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$\"\"$ .

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Since $\"\"$ , then $\"\"$

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Rewrite the equation $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Substittute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Substitute the corresponding values in $\"\"$ .

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$\"\"$ .

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Therefore, the fifth polynomial function is $\"\"$ .

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$\"\"$

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(b) Graph :Graph the function $\"\"$ , where $\"\"$ . $\"\"$

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$\"\"$

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(a) The fifth polynomial function is $\"\"$ .

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(b) Graph of the function $\"\"$ , where $\"\"$ is

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$\"\"$ .