Mathematics, 23.10.2019 20:30 nockturnal1993

Are the following statements true or false? 1. fu⃗ (a, b) is parallel to u⃗ . 2. 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. 3. if u⃗ is perpendicular to ∇f(a, b), then fu⃗ (a, b)=⟨0,0⟩. 4. if f(x, y) has fx(a, b)=0 and fy(a, b)=0 at the point (a, b), then f is constant everywhere. 5. ∇f(a, b) is a vector in 3-dimensional space. 6. the gradient vector ∇f(a, b) is tangent to the contour of f at (a, b). 7. if u⃗ is a unit vector, then fu⃗ (a, b) is a vector. 8. fu⃗ (a, b)=||∇f(a, b)||.

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Are the following statements true or false? 1. fu⃗ (a, b) is parallel to u⃗ . 2. suppose fx(a, b) a...