Graphically, find a critical point of the function

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

Using Microcalc:

- Choose
*Beginning Calculus*from the initial menu and press . - Use the arrow keys to move to the menu item
*Graph y = F(x)*, press and . - At the prompt
*F(x) =*, enter the formulax^(4/3)(x-0.1)^2 - Enter the bounds at the prompts
*x_0 =*-5*x_1 =*5*y_0 =*0*y_1 =*20

- The following graph appears to have a single critical point.
- Press and, using the arrow
keys, move to
*Change [x0, x1]*and press . - Enter the bounds at the prompts
*x_0 =*-0.2*x_1 =*0.2

- There is not much of a graph. Press
and, using the arrow keys, move to
*Change [y0, y1]*and press . - Enter the bounds at the prompts
*y_0 =*0*y_1 =*0.001

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