- #1

karush

Gold Member

MHB

- 3,269

- 5

$\tiny{243.14.7.4}$

Find all local extreme values of the given function and

identify each as a local maximum,local minimum,or saddlepoint

\begin{align*} \displaystyle

f_4(x,y)&=x^2+14x+y^2-12y+5\\

\end{align*}

saw this in the section

$\text{if we substitute the values} \\$

$\text{$f_xCa, b) = 0$ and $f_y(a, b) = 0$}\\$

$\text{ into the equation both zero.}\\$

$\text{ $f_x(a, b)(x - a)+f_y(a, b)(y - b) - (z - f(a, b)) = 0$ } $

ok i haven't done this before so kinda lost

read the section on but didn't get the derivatives

answer

$\color{red}{f_4(-7,6)}=\color{red}{-80}\\$

$\color{red}{\textit{local minimum}}$

Find all local extreme values of the given function and

identify each as a local maximum,local minimum,or saddlepoint

\begin{align*} \displaystyle

f_4(x,y)&=x^2+14x+y^2-12y+5\\

\end{align*}

saw this in the section

$\text{if we substitute the values} \\$

$\text{$f_xCa, b) = 0$ and $f_y(a, b) = 0$}\\$

$\text{ into the equation both zero.}\\$

$\text{ $f_x(a, b)(x - a)+f_y(a, b)(y - b) - (z - f(a, b)) = 0$ } $

ok i haven't done this before so kinda lost

read the section on but didn't get the derivatives

answer

$\color{red}{f_4(-7,6)}=\color{red}{-80}\\$

$\color{red}{\textit{local minimum}}$

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