Draw the graphs of the function
f(x) = x3 - 5 x + 7
and its derivative and apply the first derivative test.
- Choose Beginning Calculus from the initial menu and press
- Use the arrow keys to move to the menu item Graph y = F(y), press
- At the prompt F(x) =, enter the formula
- 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
- 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
- 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
- You can now see that to the left of the vertical line the function is
increasing and its derivative is positive.