What Does the Gradient Vector Mean Intuitively?

Kon kon india se hai🙌🙌☺️🇮🇳🇮🇳
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Eureka! Thank you very much!

The best explanation I've ever heard, thanks a lot.

thank you

when did Jeff Bezos grow hair and star explaining calculus??

is gradient somewhat like google maps showing directions??

thank you ❤

thx bro

Thank you!!

Immediately googles “rolling plains” bc I’m so cultured.

The best explanation ever on what's gradient vector. Thank you!

Awesome explanation 🙂

Not really. I don't get how a 2D plane gives you a direction to go.

Thank you! Great help for my vector cal / EM review, especially cause it helps me picture what is orthogonal to it!

It does make sense, but for those who are not familiar with the gradient, they need more graphic illustration. Most students including myself were just told that the gradient is a vector that points in the steepest ascent of any 3-D surface and how to compute it given the surface function, but we were never told or shown what the gradient vector looks like any given point on the surface and whether such vector lies in the 2-D or the 3-D space, and why it points in the direction of the steepest ascent. The easiest example was the paraboloid surface. The steepest ascent on any point on the surface is always in the direction of radial away from the vertex. I think the gradient concept needs more illustration and justification. Any video that is proactive that allows for inputting the function, computes the gradient and graphs the gradient might be a good idea. Thanks.

But then when we evaluate it at a given point what does the resultant number say? Is it the total increase in magnitude given that we've moved towards that point?

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fx(f(x,y)) gives the as fast as possible changing x direction and fy(f(x,y)) gives the as fast as possible y direction and vector of these gradient vector am i correct

Ayooo jeeff bezooooozooss is that u ?

Yes I also would like to know the why . And would you mind doing an intuitive version video of directional derivatives using the gradient ? I really want to understand that one as well . Thank you !!