$\"\"$

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The function is $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Again differentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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To find the intervals of increase and decrease, set $\"image\"$ .

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$\"\"$

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$\"\"$ cannot be equated to zero.

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$\"\"$

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Therefore intervals are $\"\"$ and $\"\"$

\

Consider a test point from the interval $\"\"$ .

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Let $\"image\"$ in $\"\"$ .

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$\"image\"$ then $\"image\"$ is decreasing in the interval $\"\"$ .

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Consider a test point from the interval $\"\"$

\

Let $\"image\"$ in $\"\"$ .

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$\"image\"$ then $\"image\"$ is increasing in the interval $\"\"$ .

\

Therefore,

\

$\"image\"$ is decreasing in the interval $\"\"$ and increasing in the interval $\"\"$ .

\

$\"\"$

\

To find the inflection points, set $\"\"$ .

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$\"\"$

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$\"\"$ cannot be equated to zero.

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$\"\"$

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

\

$\"\"$

\

$\"\"$

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Inflection point is $\"\"$ .

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$\"\"$

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The test intervals are $\"\"$ and $\"\"$ .

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Interval Test Value Sign of f(x) Conclusion

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$\"\"$ $\"image\"$ $\"\"$ Concave upward

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$\"\"$ $\"image\"$ $\"\"$ Concave downward

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$\"\"$

\

(a) $\"image\"$ is decreasing in the interval $\"\"$ and increasing in the interval $\"\"$ .

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(b) Inflection point is $\"\"$ .

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(c) $\"image\"$ is concave up in the interval $\"\"$ and concave down in the interval $\"\"$ .