Why Geogebra?
I started using Geogebra (and Desmos and Cabri Geometry and calculators) because as often as possible I want students creating their own understanding. Geogebra allows for students to manipulate and long-term create their own constructions to better understand and explore mathematical concepts.
Below is an activity that I created to help students better understand the Mean Value Theorem.
Controls that the students have are the sky blue points on the x-axis, the slider (and text box) to control the height of the rectangle, and the function itself. TRY THEM OUT.
Information that I added for clarity are the function, the Area, and the Height. I used variables and LaTeX both built in in Geogebra.