Problem:
Compare the graphs of the function

f(x) = x2

and its linearization at x = 0.65.


Visualization: Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Secants & Tangents, press and .
  3. At the prompt F(x) =, enter the formula
    x^2
  4. and use the bounds
    x0 = 0 x1 = 1
    y0 = 0 y1 = 1
  5. You will then see the graph of this function.
  6. Press .
  7. Use the arrow keys to move to Choose Base Point and press and .
  8. You will then see the graphs of the curve and a vertical line. Using the right and left arrow keys you can move the vertical line. You can use to divide the size of the move by 10.
  9. After getting the line at x = 0.65 (see bottom of screen), press and .
  10. You will now see the base point on the graph of the function. Press .
  11. Use the arrow keys to move to Draw Tangent and press and .
  12. You will now see the graphs of the function and the tangent line:

  13. After pressing , use the arrow keys to move to Zoom In and press .
  14. Press and you will see that the curve is fairly close to the tangent line:

  15. You can zoom in closer if you want to see a closer approximation. Press .
  16. You will see a blank space where Zoom In was before; use the arrow keys to move to Draw Tangent and press and .
  17. You will see the previous graph. Again, press and and you will now see that Zoom In is an option.