Find the directional derivative at (x,y) at (0,1) along the direction of the most rapid increase of f.
Thanks for helping!!
Thanks for helping!!
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This is in the direction of ∇f(0, 1) = {at (0, 1)} = <1, e^2>.
==> u = ∇f(0, 1)/||∇f(0, 1)||.
So, D_u f(0, 1)
= ∇f(0, 1) · u
= ∇f(0, 1) · [∇f(0, 1)/||∇f(0, 1)||]
= ||∇f(0, 1)||
= √(1 + e^4).
I hope this helps!
==> u = ∇f(0, 1)/||∇f(0, 1)||.
So, D_u f(0, 1)
= ∇f(0, 1) · u
= ∇f(0, 1) · [∇f(0, 1)/||∇f(0, 1)||]
= ||∇f(0, 1)||
= √(1 + e^4).
I hope this helps!