===== Linearization representation ===== ==== Theorem ==== | $X,Y$ ... Banach spaces with topology | | $f\in C(X,Y)$ | | @#55EE55: postulate | @#55EE55: $ f(x+y) = f(x) + \int_0^1\ Df(x+t\ y)\cdot y\ \mathrm d t $ | ==== Discussion ==== ^ $ f(x) = f(0) + \int_0^1\ Df(t\ x)\cdot x\ \mathrm d t $ ^ === Reference === ==== Parents ==== === Context === [[Fréchet derivative]], [[Function integral]]