Problem:
Draw the graphs of the function
f(x) = |x2 - 1|
and its derivative on the closed interval [-2, 2].
Visualization:
Using Microcalc:
- Choose Beginning Calculus from the initial menu and press
.
- Use the arrow keys to move to the menu item Graph y = F(y), press
and
.
- At the prompt F(x) =, enter the formula
abs(x^2-1)
- and use the bounds
- x0 = -2
x1 = 2
- y0 = -4
y1 = 4
- You will then see the graph of this function:
- Press
.
- Use the arrow keys to move to Function Editor and press
.
- Use the arrow keys to move to Differentiate and press
.
- At each of the next five prompts, Source, F1,
Variable, x, and Target, press
.
- Use the arrow keys to move to F2 and press
; doing this, the original function is
still available.
- At Execute, press
and you
will see the derivative of our original function in F2.
- Use the arrow keys to move to F1 <<->> F2 and press
to switch the contents of F1
and F2.
- Press
and use the arrow keys to move
to Superimpose and press
.
- At the prompt F(x) =, just press
and you will see the desired graphs: