I have read that Gradient of a scalar function points in the direction in which the function is the highest. But, according to another source, the gradient function is normal to the surface of the function, I don’t get which one it is? How can I understand the gradient function? I think of it as a 3D slope of a function at a point, but I don’t know how to incorporate that with normal to the surface!
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i think if you’re given a scalar point function
it’s just magnitude like
at x=1, y=2, z=3, f(1,2,3) = 10
but when you take gradient of that function
now it’s an infinitesimal changes to that magnitude in gradient vector directions such as i, j, k (unit vector of x, y, z)
but uh f(x,y,z) = C is a 3D surface i think
taking gradient of surface function would give you normal vector at point x y z of that surface
so when you do dot product of gradient of scalar point function and gradient of 3D surface function,
result is a scalar with magnitude being the infinitesimal change in scalar point function in direction of the normal vector of surface
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