Question

1. (a) Find the minimum value of $f\begin{pmatrix} x \\ y \end{pmatrix} = x^2 + y^2$ on the curve $x + y = 2$. Why is there no maximum? (b) Find the maximum value of $g\begin{pmatrix} x \\ y \end{pmatrix} = x + y$ on the curve $x^2 + y^2 = 2$. Is there a minimum? (c) How are the questions (and answers) in parts a and b related? *2. A wire has the shape of the circle $x^2 + y^2 - 2y = 0$. Its temperature at the point $\begin{bmatrix} x \\ y \end{bmatrix}$ is given by $T\begin{pmatrix} x \\ y \end{pmatrix} = 2x^2 + 3y$. Find the maximum and minimum temperatures of the wire. (Be sure you've found all potential critical points.) 3. Find the maximum value of $f\begin{pmatrix} x \\ y \\ z \end{pmatrix} = 2x + 2y - z$ on the sphere of radius 2 centered at the origin.

          1. (a) Find the minimum value of $f\begin{pmatrix} x \\ y \end{pmatrix} = x^2 + y^2$ on the curve $x + y = 2$. Why is there no maximum?
(b) Find the maximum value of $g\begin{pmatrix} x \\ y \end{pmatrix} = x + y$ on the curve $x^2 + y^2 = 2$. Is there a minimum?
(c) How are the questions (and answers) in parts a and b related?
*2. A wire has the shape of the circle $x^2 + y^2 - 2y = 0$. Its temperature at the point $\begin{bmatrix} x \\ y \end{bmatrix}$ is given by $T\begin{pmatrix} x \\ y \end{pmatrix} = 2x^2 + 3y$. Find the maximum and minimum temperatures of the wire. (Be sure you've found all potential critical points.)
3. Find the maximum value of $f\begin{pmatrix} x \\ y \\ z \end{pmatrix} = 2x + 2y - z$ on the sphere of radius 2 centered at the origin.

1 a find the minimum value of fbeginpmatrix x y endpmatrix x2 y2 on the curve x y 2 why is there no maximum b find the maximum value of gbeginpmatrix x y endpmatrix x y on the curve x2 y2 2 78087

Added by Tammie E.

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