find min and max

[nattt]

hi , need help with the next question:
g(x,y)=(f(x,y))^2019
i need to find the minimum and the maximum.
thank you.

 

[Deleted member 4993]

hi , need help with the next question:
g(x,y)=(f(x,y))^2019
i need to find the minimum and the maximum.
thank you.

As posted, the problem does not make sense to me (without prior information or post-information).

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[nattt]

ok,
the question is to find local minimum and maximum of the next fuction: g(x,y)=f(x,y)^2019
first i did the partial derivative:
this is what i did:
gd/dx: 2019(f(x,y))^2018 * d/xf(x,y)
gd/dy: 2019(f(x,y))^2018* d/yf(x,y)
ect.( i did gxx,gyy,gxy)
now i need to do gd/dx=0 and gd/dy=0 to fing the critical points and this is where i stuck

 

[Dr.Peterson]

Are you really told nothing at all about function f? Do you even know if it is differentiable? Clearly you have not shown the entire problem.

Look for information preceding this problem; and show us a picture of the problem as given, so we can see if there are any clues you missed.

 

[Steven G]

I hope that it is clear to you that the max of g(x,y)=f(x,y)^2019 will be the {max of f(x,y)}^2019.

Just look at y = t^2019. Assume a and b are positive, isn't it clear to you that if a<b, then a^2019 < b^2019.

Actually, if a<b, then a^2019 < b^2019.