Question

Hi, I'm new, can someone please help me with this question?

A metal disc heats up when it spins. The temperature in degrees celcius on the disc at the point (x, y) is f (x, y) = 400e^(x+y^2) . The disc has radius 1, so the boundary is given by x^2 + y^2 ≤ 1. What is the highest temperature on the disc? Where does this temperature occur? Fully justify your answer.

Answer 1

welcome to OS

Answer 2

thank you :)

Answer 3

i think you can do this one in your head :p

Answer 4

but how could I justify it then? lol

Answer 5

is it \(f (x, y) = 400e^{(x+y)^2} \)
or \(f (x, y) = 400e^{x+y^2} \)

in most part the bigger x and y are.....the bigger f is.

if it is the second one, you should look at positive x values, but with the same general idea

Answer 6

yea its the second one

Answer 7

you can do some calculus if you want. is that the point?

:p

Answer 8

I think so lol

Answer 9

I tried finding the critical points for \[f(x,y) = 400e^{x + y^{2}}\] to see if I could get a max value but I found that it doesn't exist..

Answer 10

hi

Answer 11

hi