Problem:
Graphically, find a critical point of the function

f(x) = x4/3 (x - 0.1)2.

(Example motivated by Penn and Bailey, p.50)


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph y = F(x), press and .
  3. At the prompt F(x) =, enter the formula
    x^(4/3)(x-0.1)^2
  4. Enter the bounds at the prompts
    x_0 = -5 x_1 = 5
    y_0 = 0 y_1 = 20
  5. The following graph appears to have a single critical point.

  6. Press and, using the arrow keys, move to Change [x0, x1] and press .
  7. Enter the bounds at the prompts
    x_0 = -0.2 x_1 = 0.2
  8. There is not much of a graph. Press and, using the arrow keys, move to Change [y0, y1] and press .
  9. Enter the bounds at the prompts
    y_0 = 0 y_1 = 0.001

  10. Now you will see that there appear to be at least three critical points.