Use the contour diagram of f to decide if the specified directional derivative i

Question

Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. At the point (0, 2) in the direction of vector j, At the point (-2, 2) in the direction of vector i, At the point (-1, 1) in the direction of (vector -i vector - j)/Squareroot vector 2, At the point (1, 0) in the direction of vector -j, At the point (-1, 1) in the direction of (-vector i + vector j)/Squareroot vector 2, At the point (0, -2) in the direction of (vector i - 2 vector j) Squarerot 5,

Explanation / Answer

1 ) At point ( 0 , 2) in the direction of j ,

      Moving toward heigher z values so the direction derivative is poistive.

2) At point ( - 2 , 2) IN the direction of i ,

       Moving form z = 0.8 toward z= 0.6 , So the direction derivative is negative.

3) At the point ( - 1 , 1) in the direction of (- i - j) sqrt(2) .

   Weare moving parallel to the contour at that point , so our z value would be unchanging at that instant

   So the direction derivative is zero.

4) At point ( 1 , 0) in the direction of - j.

We are moving parallel to the contour at that point , so our z value would be unchanging at that instant

   So the direction derivative is zero.

5) At point ( - 1 , 1) in the direction of (- i + j) / sqrt( 2) .

     Moving toward heigher z values so the direction derivative is poistive.

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