Example · High school
Terms
| Term | This example | Why |
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| one sided derivative |
$f_{+}^{\prime}(0) = -1$ and $f_{-}^{\prime}(0) = 1$
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| clarke generalized gradient |
$\partial f(0) = [-1, 1]$
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At $0$, the one-sided derivatives of $-\abs{x}$ are $-1$ and $1$, and its Clarke generalized gradient is $[-1, 1]$.
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| subdifferential |
$\partial f(0) = \emptyset$
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The function is concave, so no line through $(0, 0)$ lies below its graph, and it has an empty subgradients at $0$.
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