A nowhere differentiable function is a function for which no derivative exists at any point in its domain.
Nowhere Differentiable Function
See also
Blancmange Function, Differentiable, Monsters of Real Analysis, Pathological, Weierstrass FunctionExplore with Wolfram|Alpha
References
Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. "Nowhere Differentiable Functions." §5.1 in Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 107-120, 2007.Cite this as:
Weisstein, Eric W. "Nowhere Differentiable Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NowhereDifferentiableFunction.html