Use the contour diagram of f in the figure below to decide if the specified dire

Question

Use the contour diagram of f in the figure below to decide if the specified directional derivatives below are positive, negative, or approximately zero.

At point (?2,2), in direction ?i:     ?    positive    negative    approximately zero   

(b) At point (0,?2), in direction j:     ?    positive    negative    approximately zero   

(c) At point (?1,1), in direction i+j:     ?    positive    negative    approximately zero   

(d) At point (?1,1), in direction ?i+j:     ?    positive    negative    approximately zero   

(e) At point (0,?2), in direction i+2j:     ?    positive    negative    approximately zero   

(f) At point (0,?2), in direction i?2j:    ?    positive    negative    approximately zero

Use the contour diagram of f in the figure below to decide if the specified directional derivatives below are positive, negative, or approximately zero. At point (???2,2), in direction ???i: ? positive negative approximately zero (b) At point (0,???2), in direction j: ? positive negative approximately zero (c) At point (???1,1), in direction i+j: ? positive negative approximately zero (d) At point (???1,1), in direction ???i+j: ? positive negative approximately zero (e) At point (0,???2), in direction i+2j: ? positive negative approximately zero (f) At point (0,???2), in direction i???2j: ? positive negative approximately zero

Explanation / Answer

If z increases, then the directional derivative is positive.

If z is decreasing in that direction, then the directional derivative is negative.

If z is not changing, then the directional derivative is zero.

Hence,

(a) positive

(b) negative

(c) zero

(d) positive

(e) negative

(f) positive

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