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 August 7th, 2012, 02:11 AM #1 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Scalar and vector fields, calculating gradients Hi! A 2 dimensional scalar field f(x,y)=x^2 -2y^2 +x I need to find the gradient grad f of the scalar field f and what the value is at point (1,-1). I have grad f = (2x)i+(-4y)j and grad f (1,-1)= 2i+4j I now need to find the value of the derivative of the scalar field f at the point (1,-1), in the direction of the vector d=I-j. Can anyone help?
 August 7th, 2012, 02:43 AM #2 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Scalar and vector fields, calculating gradients Would this be grad f . d ? = 0
 August 7th, 2012, 03:06 AM #3 Senior Member   Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0 Re: Scalar and vector fields, calculating gradients To be the derivative in the direction of d, it would be $\text{D}_{\small d}f=(\text{grad }f)\cdot \hat{d}$, or the dot product of of the gradient of f and the unit vector of d.
 August 7th, 2012, 03:12 AM #4 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Scalar and vector fields, calculating gradients So would this be (2,4) . 1/root 2 (1,-1) = 2/root 2
 August 7th, 2012, 03:15 AM #5 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Scalar and vector fields, calculating gradients I also need to find the maximum value of the derivative of the scalar field f at the point (1,-1), and what is its direction is. And the direction of the tangent line to the contour curve f(x,y) =0 at the point (0,0).
 August 7th, 2012, 03:18 AM #6 Senior Member   Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0 Re: Scalar and vector fields, calculating gradients $2\cdot\frac{1}{\sqrt{2}}+4\cdot\frac{-1}{\sqrt{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}$
 August 8th, 2012, 02:13 AM #7 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Scalar and vector fields, calculating gradients Thanks, can you help me with the last 2 parts?
August 9th, 2012, 07:46 AM   #8
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Re: Scalar and vector fields, calculating gradients

Quote:
 Originally Posted by arron1990 Would this be grad f . d ? = 0
2- 4 is NOT 0!

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