How do I find the value of the rate of increase of the function $z=x^2+y^2$ along the direction of the given line $y=3x-1$ and in the $xy$ plane at the point $(x, y, z)=(1,2,5)$?
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2Try the directional derivative in the direction of the line. – Michael Burr Nov 18 '16 at 11:46
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Your vector is not a unit vector, so you must be wary of this. Put $f(x, y, z)=x^2+y^2-z$ Call $(x, y, z)=(1, 2, 5) = \mathbf{u}$. – Nov 18 '16 at 12:00
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You might want to use the definitions of directional derivative and the gradient. – coffeemath Nov 18 '16 at 12:17