exercise:D6b0ebd735: Difference between revisions
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\newcommand{\mathds}{\mathbb} | \newcommand{\mathds}{\mathbb} | ||
</math></div> | </math></div> | ||
Consider the function <math>f</math> defined on the closed interval | |||
<math>[4,7]</math> by | Consider the function <math>f</math> defined on the closed interval <math>[4,7]</math> by | ||
<math display="block"> | <math display="block"> | ||
\ | \begin{cases} f(x)=0, x=4, \\ f(x)=7-x, 4 < x \leq 7. \end{cases} | ||
</math> | </math> | ||
Show where this function fails to satisfy the conditions of | Show where this function fails to satisfy the conditions of Rolle's Theorem, and that is does not satisfy the conclusion. | ||
Rolle's Theorem, and that is does not satisfy the conclusion. | |||
Latest revision as of 00:05, 23 November 2024
[math]
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\newcommand{\Z}{\mathrm{\bf Z}}
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\newcommand{\conj}[1]{\overline{#1}}
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[/math]
Consider the function [math]f[/math] defined on the closed interval [math][4,7][/math] by
[[math]]
\begin{cases} f(x)=0, x=4, \\ f(x)=7-x, 4 \lt x \leq 7. \end{cases}
[[/math]]
Show where this function fails to satisfy the conditions of Rolle's Theorem, and that is does not satisfy the conclusion.