$\"\"$

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(a)

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The function is $\"\"$ .

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First evaluate the slope of tangent line.

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Slope of the tangent line : $\"\"$ .

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$\"\"$

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Slope of the tangent line is $\"\"$ .

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$\"\"$

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If $\"\"$ then $\"\"$ .

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Point of tangency is $\"\"$ .

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If $\"\"$ then slope of the tangent line is $\"\"$ .

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Point - slope form of line equation : $\"\"$ .

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Substitute $\"\"$ and point $\"\"$ in point slope form.

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$\"\"$

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$\"\"$

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Equation of tangent line is $\"\"$ .

\

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If $\"\"$ then $\"\"$ .

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Point of tangency is $\"\"$ .

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If $\"\"$ then slope of the tangent line is $\"\"$ .

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Point - slope form of line equation : $\"\"$ .

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Substitute $\"\"$ and point $\"\"$ in point slope form.

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$\"\"$

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Equation of tangent line is $\"\"$ .

\

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If $\"\"$ then $\"\"$ .

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Point of tangency is $\"\"$ .

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If $\"\"$ then slope of the tangent line is $\"\"$ .

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Point - slope form of line equation : $\"\"$ .

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Substitute $\"\"$ and point $\"\"$ in point slope form.

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$\"\"$

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$\"\"$

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Equation of tangent line is $\"\"$ .

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$\"\"$

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Graph :

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Graph the function is $\"\"$ .

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Graph the tangent lines $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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The function is $\"\"$ .

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First evaluate the slope of tangent line.

\

Slope of the tangent line : $\"\"$ .

\

$\"\"$

\

Slope of the tangent line is $\"\"$ .

\

$\"\"$

\

If $\"\"$ then $\"\"$ .

\

Point of tangency is $\"\"$ .

\

If $\"\"$ then slope of the tangent line is $\"\"$ .

\

Point - slope form of line equation : $\"\"$ .

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Substitute $\"\"$ and point $\"\"$ in point slope form.

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$\"\"$

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$\"\"$

\

Equation of tangent line is $\"\"$ .

\

\

If $\"\"$ then $\"\"$ .

\

Point of tangency is $\"\"$ .

\

If $\"\"$ then slope of the tangent line is $\"\"$ .

\

Point - slope form of line equation : $\"\"$ .

\

Substitute $\"\"$ and point $\"\"$ in point slope form.

\

$\"\"$

\

Equation of tangent line is $\"\"$ .

\

\

If $\"\"$ then $\"\"$ .

\

Point of tangency is $\"\"$ .

\

If $\"\"$ then slope of the tangent line is $\"\"$ .

\

Point - slope form of line equation : $\"\"$ .

\

Substitute $\"\"$ and point $\"\"$ in point slope form.

\

$\"\"$

\

$\"\"$

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Equation of tangent line is $\"\"$ .

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$\"\"$

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Graph:

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Graph the function is $\"\"$ .

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Graph the tangent lines $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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(a) The slopes of the tangent lines are distinct for different values of $\"\"$ .

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(b) The slopes of the tangent lines are same for few values of $\"\"$ .