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--- pow:problem4s24 [2024/03/25 03:44] – created mazur
+++ pow:problem4s24 [2024/03/28 05:27] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange|Problem 4 (due Monday, March 25) >
+A function $f:\mathbb R^2\longrightarrow \mathbb R$ has the following properties:
+a) the partial derivatives $\displaystyle \frac{\partial f}{\partial x}$ and $\displaystyle \frac{\partial f}{\partial y}$ are continuous on $\mathbb R^2$;
+b) $\displaystyle \left (\frac{\partial f}{\partial x}(x,y)\right)^2+\left (\displaystyle \frac{\partial f}{\partial y}(x,y)\right)^2\leq \frac{\partial f}{\partial x}(x,y)$ for every $(x,y)\in \mathbb R^2$;
+c) $f(x,0)=0$ for all $x\in \mathbb R$.
+Prove that $f(x,y)=0$ for all $(x,y)\in \mathbb R^2$.
+</box>
+We received only one (partial) solution, from  Beatrice Antoinette. For a complete solution see the following link {{:pow:2024sproblem4.pdf|Solution}}.