Exploring Derivatives of f(x,y)

∇f = ⟨0, 0⟩
u = ⟨cosθ, sinθ⟩ | Dᵤf = 0
z = 0 | θ = 45°
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1. How does the steepness of the Tangent Plane relate to the magnitude |∇f|?

2. Why is the Directional Derivative zero when u is tangent to a level curve?

General Lab Summary:

X₀: Y₀: θ: