Problem:
Draw the graphs of the function

f(x) = x3 - 5 x + 7

and its derivative and apply the first derivative test.

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(y), press and .
3. At the prompt F(x) =, enter the formula
x^3-5x+7
4. and use the bounds
x0 = -4 x1 = 4
y0 = -5 y1 = 15
5. You will then see the graph of this function:

6. Press .
7. Use the arrow keys to move to Function Editor and press .
8. Use the arrow keys to move to Differentiate and press .
9. At each of the next five prompts, Source, F1, Variable, x, and Target, press .
10. Use the arrow keys to move to F2 and press ; doing this, the original function is still available.
11. At Execute, press and you will see the derivative of our original function in F2.
12. Use the arrow keys to move to F1 <<->> F2 and press to switch the contents of F1 and F2.
13. Press and use the arrow keys to move to Superimpose and press .
14. At the prompt F(x) =, just press and you will see the desired graphs:

15. Press and use the arrow keys to move to Vertical Line; press and .
16. A vertical line appears on the screen which can be moved by using the left and right arrow keys. If you press then the size of the move is divided by 10. You can obtain the following graph:

17. You can now see that to the left of the vertical line the function is increasing and its derivative is positive.