? ? ? ? ? everywhere. ? 6. Suppose fx(a, b) and fy(a, b) both exist. Then there is always a direction in which the rate of change of f at (a, b) is zero. 7. The gradient vector Vf(a, b) is tangent to the contour of f at (a, b). 8. If u is a unit vector, then f(a, b) is a vector. ? 1. f (a, b) is parallel to u. 2. f (a, b) = ||V f(a, b)||. 3. If u is perpendicular to Vƒ(a, b), then ƒ (a, b) = (0,0). 4. V f(a, b) is a vector in 3-dimensional space. 5. If f(x, y) has fx(a, b) = 0 and fy(a, b) = 0 at the point (a, b), then f is constan ?

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A: Please see the below picture for detailed solution.

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A: This is a problem of Vector Calculus.

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A: Step 1:      Step 2:       Step 3:         Step 4:            Step5      Step6      Step7

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A:

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