Techlab 11.3

Instructions

• Please be patient while the program is loading. It can take up to 30 seconds to load and then run, depending on the available bandwidth. It runs much faster if you download it to your hard drive.
  
• In the box following "f(x) = " enter the equation "2*x" and check the box to its immediate right.
• Click the "Graph" button.
• Using the mouse, left-click as accurately as you can, on the x-axis at x = {-4, -3, -2, -1, 0, 1, 2, 3, 4} . A tangent line will be drawn in blue, representing the gradient of the primitive function at this value for x.
• Repeat this above and below the x-axis along the horizontal lines y = {-4, -3, -2, -1, 0, 1, 2, 3, 4}. A tangent field is produced that indicates the general shape of the primitive function.
• Left-click the "Reset Field" button. Left-click at a point anywhere on the field (often the origin is a useful place to start if possible). Click on the endpoints of the tangent line produced. Continue clicking on the endpoints of each tangent line until a continuous "curve" of the primitive function is produced.
• Try to determine the equation for the primitive function. Enter the equation you believe to be the primitive function into the box following "F(x) = " and check the box to its immediate right and click the "Graph" button again. The program will draw the graph that you have suggested (in magenta).
• Left-click at different points on the curve for F(x) to get the tangent at those points, so that you can compare the "fit". Make changes to the primitive function until you have a good "fit".
• Click the "Reset Field" button again. Click at a different starting point on the field to the one used above. Produce a continuous "curve" of the primitive function again. How does the equation for this curve differ from the one found above? Write the general anti-derivative for f(x).