$\"\"$

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The function is $\"\"$ and point $\"\"$ .

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(a)

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Draw the secant lines with $\"\"$ and $\"\"$ .

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The point $\"\"$ takes $\"\"$ - values of $\"\"$ and $\"\"$ .

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Take $\"\"$ the point is $\"\"$ .

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Take $\"\"$ the point is $\"\"$ .

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Take $\"\"$ the point is $\"\"$ .

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Draw the secant lines with the following points $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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Find the slope of secant line passing through $\"\"$ and $\"\"$ .

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Slope $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Find the slope of secant line passing through $\"\"$ and $\"\"$ .

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Slope $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Find the slope of secant line passing through $\"\"$ and $\"\"$ .

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Slope $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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(c)

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With the above observation the slope of the tangent line is greater than $\"\"$ and less than $\"\"$ , we can clearly observe it in the graph.

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On an average, the slope can be $\"\"$ approximately.

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As the point $\"\"$ approaches to the point $\"\"$ , the slope of the secant line approaches to the slope of tangents.

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Therefore to improve approximation of slope, the point $\"\"$ should approach to Point $\"\"$ .

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$\"\"$

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(a) The Graph of the function and secant lines are drawn.

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Graph:

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$\"\"$

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(b)

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The slope of secant line passing through $\"\"$ and $\"\"$ is $\"\"$ .

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The slope of secant line passing through $\"\"$ and $\"\"$ is $\"\"$ .

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The slope of secant line passing through $\"\"$ and $\"\"$ is $\"\"$ .

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(c) Slope of the tangent line is $\"\"$ approximately.