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 P(2,4) of the graph of the function:

y=x^2

Solution

2. Calculate the slope of the tangent line at the point P(0,0) of the graph of the function:

y=xe^x

Solution

3. Calculate the slope of the tangent line at the point P(\displaystyle\frac{\pi}{2},1) of the graph of the function:

y=\sin(x)

Solution

4. Calculate the equation of the line through the point P(1,2) with slope 3.

Solution

5. Calculate the equation of the line through the point P(0,1) parallel to the line:

y=-2x+5

Solution

6. Calculate the equation of the tangent line at the point P(2,5) of the graph of the function:

y=-x^2+2x+5

Solution

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

y=x^3-x-1

parallel to the tangent line at the point P(2,5) of the graph of the function:

y=-x^2+2x+5

Solution

8. The line:

y=x

intersects the parabola:

y=x^2-7x+12

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

Solution

9. The graph of the function:

y=e^x

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

Solution

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

(1,2) and (3,4)

Solution

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