Coordinate Plane Tools
Zoom In/Zoom Out/Reset Zoom: Selecting any of these tools performs the
Move: After selecting the tool, click and drag on the coordinate plane
to move it in the view screen. This tool remains active until another tool is
Trace: A graph must be displayed to enable the tool. Click on any
point along a graph to view the coordinates of that point. Drag along the graph
to view other coordinates. This tool remains active until another tool is
Draw Graph: You must begin by creating a polynomial graph on the
Modify Graph: This tool allows you to move the roots and change the
stretch of your graph. Click once to begin, and click Done Modifying to
Clear Graph: This tool clears the entire workspace.
Approximate: Select this tool to create an approximate tangent.
(Note: You cannot create an approximate tangent if the actual tangent is
Actual: Select this tool to display the tangent at a point. If no
tangent is displayed, you will need to select one.
Clicking either slope button will show/hide the respective slope.
Approximate: Select this tool to create approximate derivative curves.
Depending on your original graph, you can create up to a fourth derivative.
(Note: You cannot create an approximate derivative if the corresponding
actual derivative is displayed.)
y', y'', etc.: To draw the second, third, etc.
derivatives, click on the corresponding button. You can also click any button to
hide/show that graph.
Actual: Select this tool to display the graph of the first derivative.
y, y', y'', etc.: Click any button to show/hide
Approximate: Select this tool to approximate the area under the curve
using rectangles. (Note: You cannot create an approximate area if the
actual area is displayed.)
Actual: Select this tool to display the area between two points. If
limits are not selected, you will need to select them.
Clicking either area button will show/hide the respective area.
Create a graph with roots approximately at –12, –1, 10, and 10. This means
there will be a double root at (10,0). Stretch the graph so the
y-intercept is approximately 1.
One at a time, draw approximate tangents where x is approximately –8,
–3, and 5.
Draw approximations for all possible derivatives.
Select –13 and –3 as your lower and upper limits, respectively. Then, change
the number of rectangles to 5. Create each of the following approximations:
The left corner of each rectangle is touching the graph.
The right corner of each rectangle is touching the graph.
The midpoint of the side of each rectangle is touching the graph.
Adjust all rectangles to create your best approximation.
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