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9.1. Define f : R² R by f(x,y) = = - 2 x2 + y2 , and f(0,0) = 0. Prove that f is Lipschitz. (Note and hint: This is the same function as problem 5.1 (a) and in lecture for a different purpose. f is not a C¹ function, but you can follow the proof from lecture that C¹ functions on bricks are Lipschitz. Namely, if the derivative of f is bounded, you can integrate the derivative you can show that its derivative is bounded and integrate it. The origin is a special case because f is not differentiable there; although it does have directional derivatives.)

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Real Analysis Problem
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