I found this video is really helpful for my studying about calculus 2 in uni. Could you share that geogebra animation, I really want to learn more about animating in geogebra! After all, thank you so much for your work!
If the directional derivative is the scalar product with a turning unitary vector, it's mean that 2 points which have the same gradient on 2 different curve will have necessarly the same directional derivative in each direction at that given point ? Probably because the 2 different curve are the same LOCALLY ? -- altough intuitively I would think it could be different and depend on the law of evolution of it's own curve.
Yes looks like you’re on the right track. If gradient f at (a,b) has the same value as gradient g at (c,d), then locally f and g look the same, and if u is any unit vector, then the directional derivative for f at (a, b) in the direction of u will match the directional derivative for g at (c,d) in the direction of u. This is because the directional derivative is just the scalar product of the gradient with u.
Is the gradient vector really perpendicular to slope ? He is in the plane X-Y and his magnitude is the slope of the surface curve at the given point ? if we take this magnitude for the component in Z, we have a vector perpendicular, let's say rather normal, to the surface curve ?
Thank you so much! This helped me understand directional derivatives a lot more with the visualizing.
Glad it was helpful!
How did you do the animation?
I used Geogebra. It’s crazy how much it can do for free.
I found this video is really helpful for my studying about calculus 2 in uni. Could you share that geogebra animation, I really want to learn more about animating in geogebra! After all, thank you so much for your work!
Glad it was helpful! Sure here’s the Geogebra link.
www.geogebra.org/m/e7vztr4d
If the directional derivative is the scalar product with a turning unitary vector, it's mean that 2 points which have the same gradient on 2 different curve will have necessarly the same directional derivative in each direction at that given point ? Probably because the 2 different curve are the same LOCALLY ? -- altough intuitively I would think it could be different and depend on the law of evolution of it's own curve.
Yes looks like you’re on the right track. If gradient f at (a,b) has the same value as gradient g at (c,d), then locally f and g look the same, and if u is any unit vector, then the directional derivative for f at (a, b) in the direction of u will match the directional derivative for g at (c,d) in the direction of u. This is because the directional derivative is just the scalar product of the gradient with u.
thanks man
thank you!!!!!
Glad it was helpful!
😀
spend 2 hours trying to figure out why gradient is perpendicular to slope
Not bad, sucks when you’ve got other stuff to do, but putting that time in will pay off. Glad to hear the video was helpful!
Is the gradient vector really perpendicular to slope ? He is in the plane X-Y and his magnitude is the slope of the surface curve at the given point ? if we take this magnitude for the component in Z, we have a vector perpendicular, let's say rather normal, to the surface curve ?