exercise:74ff487458: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow}...") |
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\newcommand{\mathds}{\mathbb} | \newcommand{\mathds}{\mathbb} | ||
</math></div> | </math></div> | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li>The equation <math>x^3 + y^3 - 6xy = 0</math> implicitly defines a differentiable function <math>f(x)</math> whose graph | ||
The equation <math>x^3 + y^3 - 6xy = 0</math> | |||
implicitly defines a differentiable function <math>f(x)</math> whose graph | |||
passes through <math>(3,3)</math>. Compute <math>f^\prime (3)</math>.</li> | passes through <math>(3,3)</math>. Compute <math>f^\prime (3)</math>.</li> | ||
<li>How many differentiable functions <math>f(x)</math> having a small | <li>How many differentiable functions <math>f(x)</math> having a small | ||
interval about the number <math>3</math> as a common domain are | interval about the number <math>3</math> as a common domain are | ||
implicitly defined by the equation in | implicitly defined by the equation in (a)?</li> | ||
<li>Compute <math>f^\prime (3)</math> for each of them.</li> | <li>Compute <math>f^\prime (3)</math> for each of them.</li> | ||
</ul> | </ul> | ||
Latest revision as of 23:34, 22 November 2024
[math]
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[/math]
- The equation [math]x^3 + y^3 - 6xy = 0[/math] implicitly defines a differentiable function [math]f(x)[/math] whose graph passes through [math](3,3)[/math]. Compute [math]f^\prime (3)[/math].
- How many differentiable functions [math]f(x)[/math] having a small interval about the number [math]3[/math] as a common domain are implicitly defined by the equation in (a)?
- Compute [math]f^\prime (3)[/math] for each of them.