$\"\"$

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(a)

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The function is $\"\"$ .

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Find the secant line passing through the points $\"\"$ and $\"\"$ .

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The equation of a secant line passing through two points is $\"\"$

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$\"\"$

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The equation of secant line is $\"\"$ .

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$\"\"$

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(b)

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Mean value Theorem :

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If $\"\"$ is continuous on $\"\"$ and differentiable on open interval $\"\"$ , then there exists a number $\"\"$ in $\"\"$ such that $\"\"$ .

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The function $\"\"$ is continuous on the interval $\"\"$ and differentiable on the interval $\"\"$ .

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So there exists a number $\"\"$ in $\"\"$ such that $\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$

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The value of $\"\"$ in the interval $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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(c)

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Find the equation of tangent line passing through $\"\"$ and is parallel to the secant line.

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The secant line equation is $\"\"$ .

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$\"\"$

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Compare the above equation with the slope intercept form $\"\"$ .

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The slope of the secant line is $\"\"$ .

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Point slope form of the equation is $\"\"$ .

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$\"\"$

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Therefore, the equation of tangent line is $\"\"$ .

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$\"\"$

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(d)

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Graph the function and tangent line $\"\"$ .

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$\"\"$

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$\"\"$

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(a) The equation of secant line is $\"\"$ .

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(b) The value of $\"\"$ in the interval $\"\"$ is $\"\"$ .

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(c) The equation of tangent line is $\"\"$ .

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(d)

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$\"\"$ .