First & Second Derivative Tests
- Author:
- Jason Miner
Enter a function f(x) and use the x slider to move the point P along the curve f. Note the location of the corresponding point on the graph of f'(x). Where is the red point when P is on the part of f that is decreasing or decreasing? When the red point is on the x-axis, what is happening on the graph of f? When the red point is at a maximum or minimum of f'(x), what is happening on the graph of f?
Note the location of the corresponding point on the graph of f''(x). Where is the green point when P is on the part of f that is concave up or concave down; where is the red point at this instant? When the green point is on the x-axis, what is happening on the graph of f; where is the red point at this instant?
To change the viewing window, hold the shift button and left-click to drag the graph or use the scroll wheel to zoom in/out. You can also adjust the axes by holding the shift button and left-click on the axis you want to change.