Compare the graphs of the function
f(x) = x2
and its linearization at x = 0.65.
- Choose Beginning Calculus from the initial menu and press
- Use the arrow keys to move to the menu item Secants & Tangents,
- At the prompt F(x) =, enter the formula
- and use the bounds
- x0 = 0 x1 = 1
- y0 = 0 y1 = 1
- You will then see the graph of this function.
- Press .
- Use the arrow keys to move to Choose Base Point and press
- 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
- After getting the line at x = 0.65 (see bottom of screen), press
- You will now see the base point on the graph of the function. Press
- Use the arrow keys to move to Draw Tangent and press
- You will now see the graphs of the function and the tangent line:
- After pressing
, use the arrow keys to move to
Zoom In and press .
- Press and you will see that
the curve is fairly close to the tangent line:
- You can zoom in closer if you want to see a closer approximation.
- You will see a blank space where Zoom In was before; use the
arrow keys to move to Draw Tangent and press
- You will see the previous graph. Again, press
and you will now see that
Zoom In is an option.