  In this paper we prove an inverse function theorem in derived differential
geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces
which is a quasi-isomorphism at a point has a local homotopy inverse. This
theorem simultaneously generalizes the inverse function theorem for smooth
manifolds and the Whitehead theorem for $L_\infty$ algebras. The main
ingredients are the obstruction theory for $L_\infty$ homomorphisms (in the
curved setting) and the homotopy transfer theorem for curved $L_\infty$
algebras. Both techniques work in the $A_\infty$ case as well.
