13 lines
316 B
TeX
13 lines
316 B
TeX
\beginsection 18.1
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Let $f$ be as in Theorem 18.1. Show that if $-f$ assumes its maximum at
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$x_0\in[a,b]$, then $f$ assumes its minimum at $x_0$.
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\medskip
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Since $x_0$ is a maximum for $-f$ we have
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$$-f(x_0)\ge-f(x).$$
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Multiply through by $-1$ to get
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$$f(x_0)\le f(x).$$
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We observe that $x_0$ is a minimum for $f$.
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