Mean Value Theorem and Rolle's Theorem (in R!)
This annotated code visually demonstrates and explains the Mean Value Theorem and Rolle's Theorem. It corresponds with Section 5.4.4 in the Gill book.
Directions: (1) Scroll to the bottom and click "Activate Console". This will allow you to copy and paste the code, line by line, into the console. Make sure you run each line in the order the appear, as lines later in the code rely upon lines earlier in the code.
(2) You can enlarge the console space by dragging the horizontal line upward.
(3) When you finish running the code as is, feel free to change the function, the estimation point, and the bounds. This will allow you to try out different functions and intervals until you feel comfortable with both the Mean Value Theorem and Rolle's Theorem. When you reload the website, it should reset to the original code.
Note: Make sure you change all relevant parts of the code when you change the function. This means changing the function AND changing the derivative of the function. If you don't do that, things will go horribly awry. (Well, nothing will make sense, anyway.) So be careful in your editing!
Directions: (1) Scroll to the bottom and click "Activate Console". This will allow you to copy and paste the code, line by line, into the console. Make sure you run each line in the order the appear, as lines later in the code rely upon lines earlier in the code.
(2) You can enlarge the console space by dragging the horizontal line upward.
(3) When you finish running the code as is, feel free to change the function, the estimation point, and the bounds. This will allow you to try out different functions and intervals until you feel comfortable with both the Mean Value Theorem and Rolle's Theorem. When you reload the website, it should reset to the original code.
Note: Make sure you change all relevant parts of the code when you change the function. This means changing the function AND changing the derivative of the function. If you don't do that, things will go horribly awry. (Well, nothing will make sense, anyway.) So be careful in your editing!