Differentiable curve

Let f (x, y) = x² + y² and let λ (t) = (x (t), y (t)) be a differentiable curve whose image is contained in the level curve f (x, y) = 1, that is, for all t in the domain of λ, f (x (t), y (t)) = 1 (give an example of such a curve). Let λ (t₀) = (x₀, y₀). Prove that λ '(t₀), ∇f (x₀, y₀) = 0. Interpret geometrically.

Suggestion: for all t in the domain of λ, (x (t))²+ (y (t))² = 1; derive from t and make t = t₀)

Someone? I really need some help with this

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Differentiable curve

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