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Soit \(f : {\R^2} \to \R\) de classe \(\mathcal{C}^2\). Démontrer que : \[f(a+h,b+k) = f(a,b) + \left( h\frac{\partial f}{\partial x} + k\frac{\partial f}{\partial y} \right)(a,b) + \frac 12 \left( h^2\frac{\partial^2 f}{\partial x^2} + 2hk\frac{\partial^2 f}{\partial x \partial y} + k^2\frac{\partial^2 f}{\partial y^2} \right)(a,b) + o(h^2+k^2).\]