Please type in Geogebra and show what to type in each row of Geogebra.
Please show what to type in Geogebra to graph.
Your final graph should be something like this, but using your own surface:
1. A number from 0 to 8 that shows how many of the requirements (listed below) you accomplished.
2. All lines of your entries (what you typed on Geogebra, not what it displayed).
3. One screenshot of your final 3D graph. You must understand all components involved in this assignment (partial derivatives, gradient, r't), their orthogonality, tangent plane equation, etc.). Many of you have most of them already done.
Requirements:
1. Graph the surface.
2. Define a curve r(t) on that surface.
3. Define a point A on that curve (I recommend you choose this point in such a way that you can use each of its components separately).
4. Compute the partial derivatives of the function at that point A.
5. Construct and graph the gradient vector at A.
6. Graph the derivative r'(t) of the curve at A.
7. Graph the tangent line to the surface at A.
8. Animate your graph so that as A moves on the curve, the gradient and the derivative move with it.
You can add any steps that will help you complete the above requirements.
Your final graph should be something like this, but using your own surface.