Problem:
Compare the graphs of the function
f(x) = x2
and its linearization at x = 0.65.
Visualization:
Using Microcalc:
- 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 formula
x^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.