# Assignments

The assignments below are meant to practice the following:
a. calculating the equation of a line through a given point and with a given slope;
b. calculating the equation of a line through two given points;
c. calculating the tangent line at a point of a graph of a function.

1. Calculate the slope of the tangent line at the point  of the graph of the function:

Solution

2. Calculate the slope of the tangent line at the point  of the graph of the function:

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3. Calculate the slope of the tangent line at the point  of the graph of the function:

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4. Calculate the equation of the line through the point  with slope .

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5. Calculate the equation of the line through the point  parallel to the line:

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6. Calculate the equation of the tangent line at the point  of the graph of the function:

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7. Calculate the equation of the tangent line(s) of the graph of the function:

parallel to the tangent line at the point of the graph of the function:

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8. The line:

intersects the parabola:

in two points A en B.
The tangent lines at these points intersect in a point C.
Calculate the coordinates of C.

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9. The graph of the function:

intersects the -axis in point A.
The tangent line at this point of the graph intersects the -axis. Calculate the coordinates of this intersection point.

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10. Give the equation of the line through the points:

and

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