Question: Explain conceptually (using a paragraph and a picture) why we know the gradient vector for a function f(x,y) is orthogonal to any level curve f(x,y)

Explain conceptually (using a paragraph and a picture) why we know the gradient vector for a function f(x,y) is orthogonal to any level curve f(x,y) = k. Then make a vector-calculus argument by showing that an appropriate pair of vectors have a dot product of 0.

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