Compare the graphs of the function

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*, press and . - At the prompt
*F(x) =*, enter the formulax^2 - 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 and . - 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.
- After getting the line at x = 0.65 (see bottom of screen), press and .
- 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 and . - 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. Press .
- You will see a blank space where
*Zoom In*was before; use the arrow keys to move to*Draw Tangent*and press and . - You will see the previous graph. Again, press
and
and you will now see that
*Zoom In*is an option.