AB Calculus - Hardtke

GeoGebra Lab 1: Tangent/Secant Name

Due: 20 pts possible

Take care to read & complete each step carefully. Ms. H will correct your two files next time we are in the lab. You could lose a point for any step you do not complete as directed, so you might want to check-off steps as you complete them.

PART A:

  1. Open a new GeoGebra worksheet. In the input bar, type the function f(x) = 0.2x^3 + x^2 – 1 and enter. Right click on the graph of the function and choose Object Properties to make the graph BLUE and its Style thicker.
  2. Select the New Point tool and click anywhere on the graph of f. Right click to name this point A and color it RED.
  3. Select the Tangent Line tool and click on the point A and then the function f. Right click to make this tangent line RED and its Style any choice or thickness that differs from the function f.
  4. Select the Slope tool and click the tangent line. In the Algebra View, click the radio-button circle next to m to hide the slope (since we want to use the numerical value, but no longer need to see the rise/run triangle in the graphic view).
  5. Select the Text tool and enter "Slope of Tangent: " + m (or select m from the object pull-down menu). Increase the size of this text and color it RED.
  6. If you haven’t already done so, save your file as Lab 1A in your own directory
  7. Select the New Point tool and click on the graph of f to create a second point. Right click to label it B and color it GREEN.
  8. Select the Line Through 2 Points tool and click on the points A and B. Right click to make this secant line GREEN and and its Style any choice or thickness that differs from the function f and the tangent line.
  9. Select the Slope tool and click the secant line. In the Algebra View, click the radio-button circle next to m1 to hide the slope (since we want to use the numerical value, but no longer need to see the rise/run triangle in the graphic view).
  10. Select the Text tool and enter "Slope of Secant: " + m_1 (or select m_1 from the object pull-down menu). Increase the size of this text and color it GREEN.
  11. Select the Text tool and enter this title/direction box(es), “How can the slope of a secant approximate the slope of a tangent? Drag point B toward A and compare the slopes!” Make this text BLUE and resize and relocate it as desired.
  12. If needed, move the two slope text boxes away from the graph and place them in some attractive alignment.
  13. Verify your work by dragging point A to various locations. Each time, drag B closer to A and compare the slope of the secant to the slope of the tangent.
  14. Select the Text tool . In small black text in the lower right corner of your window, type your answer to this question: is it ever possible for the slope of the secant to equal the slope of the tangent when B is not close to A?
  15. Before saving your final version of file Lab 1A, move A and B apart so they will be distinct for your next

PART B:

The following steps are going to change your file and you should Save-As Lab 1B.

  1. Now double click on the equation of function f and edit it to become 3sin(x/2).
  2. Click on Settings from the Options Menu. In this dialogue box, select Graphics and then the X-axis Tab. Check the box to the left of Distance and then in the pull-down menu, select π2 as your choice. (Your x-axis should now have tick marks and labels at every multiple of π2.)
  3. Edit or delete & recreate the small black text box in the lower right corner of your window to answer this question: when you drag point A everywhere along f, what is the range of values for the slopes of the tangents at all points?
  4. Let’s see how you would compute a slope if not allowed to use the GeoGebra Slope Tool. First you need to get the x and y coordinates of points A and B as variables. To get the x-coordinate of point A, in the entry line, type x1 = x(A).
  5. Likewise, enter y1 = y(A) x2 = x(B) y2 = y(B)
  6. Now enter mSecant = (y2 – y1)/(x2 – x1). Did you get the same value as shown by the slope tool? Is your measurement dynamic when you drag point B?
  7. To also keep this version of your file, Save-As Lab 1B in your own directory.