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What is local maxima/minima in differentiation and calculus?
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A necessary condition that a differentiable function $f(x)$ has a local maximum (minimum) at $x=c$, that is, $f(x) \leq f(c),(f(x) \geq f(c))$ in a neighborhood $c-\delta \leq x \leq c+\delta($ $\delta>0$ ) of $c$, is $f^{\prime}(c)=0$.
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