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> There exist functions of a single real variable that have derivatives at the origin that are all zero, yet are nonzero The function that is equal to 0 for x<
by petters 7y ago
> There exist functions of a single real variable that have derivatives at the origin that are all zero, yet are nonzero
The function that is equal to 0 for x<1 and equal to 1 otherwise also satisfies this.
- messe 7y agoThe more interesting statement is: > There exist smooth functions of a single real variable that have derivatives at the origin that are all zero, yet are nonzero https://en.wikipedia.org/wiki/Non-analytic_smooth_function https://en.wikipedia.org/wiki/Non-analytic_smooth_function
- posterboy 7y agofyi, that's the heavyside function