Intermediate Value Theorem
- Author:
- Daniel Loghin
For all (red) y between f(a) and f(b) there exists c in [a,b] such that f(c)=y.
Equivalently, the (blue) image im f=f([a,b]) contains the (red) interval J.
This statement fails if f is discontinuous!
Slide c along the x-axis to see if you can find a value such that the blue dots f(c) cover the big red dot labelled y. Press the refresh button (top right) to start another experiment.
Other options:
1. Slide a,b to change the interval under consideration.
2. Change f(x): refresh picture then enter in the input field another function definition, e.g., f(x)=x^2. (You may have to grab and move the image to shake off the blue dots from the previous experiment - click on the last button in the toolbar, move the image, then click on the first button in the toolbar).