This is a bit counterintuitive to me that the gradient vector is always normal to the level curve(adsbygoogle = window.adsbygoogle || []).push({});

and the level surface.

lets say we have a function f(x,y)=z

then the gradient is,

f(x,y) partial derivative with respect to x*i +f(x,y) partial derivative with respect to y*j

what we actually get is,

dz/dx*i+dz/dy*j=grad_f(x,y)

then,

[(dz/dx*i)+(dz/dy)*j]/sqrt((dz/dx*i)^2+(dz/dy*j)^2)

this is always perpendicular to the level curve. But why does that direction always maximize the function?

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# Gradient question

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