A circular hot plate given by the relationship $x^2 + y^2 \leq 4$ is heated according to the spatial temperature function $T(x,y) = 10 - x^2 + 2x - 4y^2$. Find the hottest temperatures on the plate and the points at which they occur.
I get $D=0$ and thats suppose to be F.M.L is that normal? Usually you are suppose to get $D<0$ or $D>0$ ....$D$ is the 2nd derivative test btw.
I got $Fx=-2x+2-2x\lambda$
$F \lambda= x^2+ y^2=4$
I am using Lagrange Multiplier...I hope I am not screwing up on the system of equations...ive done this over and over 4 times with different isolations...
I get $\lambda= -4, \quad x=-1/3, \quad y=1.97$
Kinda confused about where I am screwing up..
I am also confused with this question, they are all optimization...
[a]: mixedmath removed these links, but keeps this faux-comment for posterity
A rectangular topless box of volume $12$ m$^3$ is constructed such that the material for the back and bottom costs 2 times as much as the other three sides. What dimensions of the box will minimize the total cost?
With this Last question I am able to get $L*W*H=12$
Also I am able to get that if $Z=$ material for 1 side and $Y=$material for bottom...
then I have $5z+2y=$ Cost
Now I am lost because to use LaGrange multiplier I need a bound..
I have made the volume function my $G(W,h,L)$ and $k=12$ and let the cost function be my function to minimize and solve for