The Derivative Definitions applet is a copy of the Secant/Tangent applet, but adds another set of calculations and labels to display the difference quotient in the form. #Construct segment trisector gsp5 codeTo label the tick marks without showing the points, JSP code was added to create hidden captions for each point with the FixedText construction, then attach each caption with a point using the PeggedText construction. In Sketchpad, when a point is hidden its label is also hidden. In GSP one button can toggle between hide and show, but in JSP separate buttons are required. Construct this as a locus of points the same way the tangent line was constructed. The secant line will be the locus of points (r, y) such that y = f(a) + m sec(r – a) for all r ∈. You should see the graph of the tangentline.Ĭonstruct the secant line from (a, f(a)) to (a + h, f(a + h)).Īgain, Select the interval and Construct a point on this segment and label it "a + h." Select the points (0, 0), (0, 1) and a + h in that order and Measure the ratio and label the ratio "a + h." Calculate 0.02(a+h) 4 – (a + h) 2 + 3(a + h) + 1, and label the calculation "f(a + h)." Select a + h and f(a + h) and Plot as (x, y).Ĭalculate m sec using a, f(a), a + h and f(a+h). Then Select the plotted point, the point q on the x-axis and the interval and Construct the locus. Select the ratio q and the latest calculations and Plot as (x, y). Label the ratio "q." Calculate f(a) + m tan(q – a). Select the interval and Construct a point on this segment and label it "q." Select the points (0, 0), (0, 1) and q in that order and Measure the ratio. Label this point as (a, f(a)).Ĭalculate 0.08a 3 – 2a + 3 and label the measurement m tan, which label is typed as "m." Now construct the tangent line as a locus. This ratio will be the coordinate of a label the ratio "a." Calculate 0.02a 4 – a 2 + 3a + 1, and label the calculation "f(a)." Select a and f(a) and Plot as (x, y). Select the interval and Construct a point on this segment and label it "a." Select the points (0, 0), (0, 1) and a in that order and Measure the ratio. The tangent line is the linearization at x = a consisting of points (q, f(a) + m tan(q – a)) for all q ∈. It will be useful to create a new custom tool based upon the value p and the calculation f(p).Ĭonstruct the line tangent to the curve at (a, f(a)). Then select the plotted point (p, f (p)), the point p on the x-axis and the interval and Construct the locus. This ratio will be the coordinate of p label the ratio "p." Calculate 0.02p 4 – p 2 + 3p + 1, and, if you wish, label the calculation "f(p)." Select p and f(p) and Plot as (x, y). Select the interval and Construct a point on this segment and label it "p." Select the points (0, 0), (0, 1) and p in that order and Measure the ratio. If you do not construct a domain, then the graph produced by JSP may be less than you expected. The segment connecting points (–2, 0) and (6, 0) as constructed above will serve as the domain. 02x 4 – x 2 + 3x + 1 as the locus of plotted points.Ĭonstruct a domain for the function. Tick marks are easy to construct if a custom tool is made. Make tick marks by translating every point on each axis ±5 pixels perpendicular to the axis, then construct segments connecting the axis points to their translations. Hide the original coordinate system axes. These segments are the displayed x– and y–axis. The labels will be hidden along with the points, but new labels will be attached later.Ĭonstruct the segment connecting points (–2, 0) and (6, 0), then Construct the segment connecting points (0, –10) and (0, 10). Label this point "–10." Likewise Plot as (x,y) and label all integer points on the axes. Select parameters 0 and –10 and Plot as (x, y). The GSP coordinate system has labeled axes with tick marks but the labels and tick marks will not be displayed by JSP, so we must create our own. Setup a coordinate system with labeled axes.ĭefine a coordinate system, then Select the coordinate system and set the line width to Thick so JSP will show a grid instead of merely "dot paper." The details below elaborate upon a few features of the GSP constructions, and how the JavaSketchpad code was edited to produce the final applet. The tool's script can be displayed and printed, and with experience, the steps in the script can be associated with the proper Sketchpad constructions. One way to document a Geometer's Sketchpad construction is to Show All Hidden from the Display menu, Select All from the Edit menu, then Create New Tool from the Custom Tool menu.
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