Draw the graphs of the function

and its derivative and apply the first derivative test.

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 formulax^3-5x+7 - and use the bounds
- x0 = -4 x1 = 4
- y0 = -5 y1 = 15

- 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: - Press and use the arrow keys to
move to
*Vertical Line*; press and . - 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:
- You can now see that to the left of the vertical line the function is increasing and its derivative is positive.