diff options
Diffstat (limited to 'macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex')
-rw-r--r-- | macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex | 48 |
1 files changed, 48 insertions, 0 deletions
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex new file mode 100644 index 0000000000..0bb90e4ec6 --- /dev/null +++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex @@ -0,0 +1,48 @@ +\sethandouttitle{Maximum and Minimum Values} + +\allhandoutinfo{} + +\begin{enumerate} + + + \item Sketch the graph of a function $f$ that is continous on $[1,5]$ and has an absolute minimum at 2, + absolute maximum at 3, and a local minimum at 4. + + \item \begin{enumerate} + \item Sketch the graph of a function that has a local maximum at 2 and is differentiable at 2. + \item Sketch the graph of a function that has a local maximum at 2 and is continuous but not differentiable at 2. + \item Sketch the graph of a function that has a local maximum at 2 and is not continuous at 2. + \end{enumerate} + + + \item Sketch the graph of $f$ and use your sketch to find the absolute and local maximum and minimum values of $f$. + \begin{enumerate} + \item $\displaystyle f(x) = \frac{1}{2}(3x-1), \quad x \leq 3$. + \item $f(x) = \sin(x), \quad 0 \leq x < \pi/2$. + \item $f(x) = \ln(x), \quad 0<x \leq 2$. + \item $f(x) = 1 - \sqrt{x}$. + \end{enumerate} + + \item Find the critical numbers of the function. + \begin{enumerate} + \item $\displaystyle f(x) = 4+ \frac{1}{3}x - \frac{1}{2}x^2$. + \item $\displaystyle g(y) = \frac{y-1}{ y^2 - y + 1 }$. + \item $f(\theta) = 2 \cos \theta + \sin^2 \theta$. + \item $f(\theta) = x^2 e^{-3x}$. + \end{enumerate} + + \item Find the absolute maximum and minimum values of $f$ on the given interval. + \begin{enumerate} + \item $f(x) = 12+4x-x^2$ on $[0,5]$. + \item $f(t) = t \sqrt{4-t^2}$ on $[-1,2]$. + \item $f(t) = 2 \cos t + \sin 2t$ on $[0,\pi/2]$. + \item $f(x) = x e^{-x^2/8}$ on $[-1,4]$. + \item $f(x) = \ln(x^2+x+1)$ on $[-1,1]$. + \end{enumerate} + + + +\end{enumerate} + + + |