- #1

karush

Gold Member

MHB

- 3,269

- 5

$$f(x,y,z)=\sin(x^2+y^2)\cos(z)$$

$\text{subject to the constraints} $

$$\text{$x^2+y^2=4t, 0\le t\le\pi$, and $z=\frac{\pi}{4}$}$$

$\text{Classify each extremum as a minimum or maximum.}$

\begin{align*} \displaystyle

f_7(x,y,z)&=\sin(4t)\cos\left(\frac{\pi}{4}\right)\\

&=\frac{\sqrt{2}}{2}\sin(4t)\\

f_7^\prime&=2\sqrt{2}\cos(4t)\\

&\textbf{got lost here}\\

\therefore t&=\color{red}{\frac{\pi}{8} , \textit{min}}

\end{align*}