A standard method of constructing functions which lack this property involves relying on the Baire category theorem.
A standard method of constructing functions which lack this property involves relying on the Baire category theorem. The existence of a unique function that is the graph of the locus at some point of a function with this property is guaranteed via the implicit function theorem. A function which has continuity and this property is a homeomorphism whose inverse also has continuity and this property, by the inverse function theorem. The degree to which a function possesses this property defines its smoothness class. Despite being everywhere continuous, the Weierstrauss function lacks this property everywhere, and in the complex plane, to have this property to infinite order is identical to obeying the Cauchy-Riemann equations and being analytic. For 10 points, identify this property which for a real-valued function f is equivalent to saying that the limit of f of x plus h minus f of h over h exists as h goes to zero.
A standard method of constructing functions which lack this property involves relying on the Baire category theorem.
differentiable