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Unformatted text preview: f in the direction of the unit vector u is • ∇ = ) , ( ) , ( y x f y x f D u u #28 Properties of the Gradient Let f be differentiable at the point (x,y) 1. If ) , ( y x f ∇ = then D ) , ( y x f u =0 for all u 2. The direction of maximum increase of f is given by ) , ( y x f ∇ . The maximum value of D ) , ( y x f u =0 is ) , ( y x f ∇ . 3. The direction of minimum increase of f is given by  ) , ( y x f ∇ . Then minimum value of D ) , ( y x f u is  ) , ( y x f ∇ . #32 Theorem 12.12 Gradient is Normal to Level Curves If f is differentiable at ( 29 , y x and f ∇ ( 29 , y x ≠ 0 then f ∇ ( 29 , y x is normal to the level curve through ( 29 , y x . #56 Note: The definitions and properties of directional derivatives and gradients can be extended to functions of three or more variables as seen on page 892....
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 Spring '12
 PamelaSatterfield
 Calculus, Derivative, Gradient, Level set

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