If $f$ has a minimum value at $c,$ show that the function $g(x)=-f(x)$ has a maximum value at $c .$
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If $f$ has a local minimum value at $c,$ show that the function $g(x)=-f(x)$ has a local maximum value at $c .$
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If $f$ has a local minimum value at $c$, show that the function $ g(x) = - f(x) $ has a local maximum value at $c$.
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