- #1
Odyssey
- 87
- 0
Greetings, can you guys please help me with my assignment??
I am supposed to find and classify all critical points of the function f(x,y) = (sin x)(cos y)
Now I took the first partials with repsect to x and y and they are (cos x)(cos y) = 0 and (-sin x)(sin y) = 0, respectively.
Now I know fx = 0 when either cos x = 0 or cos y = 0 and cos x = 0 when x is pi/2, -pi/2, 3pi/2, -3pi/2, ...
and fy = 0 when either sin x = 0 or sin y = 0 and sin x = 0 when x = kpi, k being integers...
But I don't know if there are infinitely many critical points or no critical points?? If there are infinitely many, where are they at??
Thanks for the help!
I am supposed to find and classify all critical points of the function f(x,y) = (sin x)(cos y)
Now I took the first partials with repsect to x and y and they are (cos x)(cos y) = 0 and (-sin x)(sin y) = 0, respectively.
Now I know fx = 0 when either cos x = 0 or cos y = 0 and cos x = 0 when x is pi/2, -pi/2, 3pi/2, -3pi/2, ...
and fy = 0 when either sin x = 0 or sin y = 0 and sin x = 0 when x = kpi, k being integers...
But I don't know if there are infinitely many critical points or no critical points?? If there are infinitely many, where are they at??
Thanks for the help!