Finding Local Extrema and Critical Points for f(x,y)=ysin(x)

[oceansoft]

Find and classify all local minima, local maxima and saddle points for the function
f(x,y)=ysin(x)

i can do this question however i am having problem with finding the x and y intercepts i get

fx= ycos(x) and fy=sin(x)
0=ycos(x) and 0=sin(x)

i start to have problem now after someone can tell me how to find the intercepts i should be fine with the rest of the question thanks.

 

[LCKurtz]

Find and classify all local minima, local maxima and saddle points for the function
f(x,y)=ysin(x)

i can do this question however i am having problem with finding the x and y intercepts i get

fx= ycos(x) and fy=sin(x)
0=ycos(x) and 0=sin(x)

i start to have problem now after someone can tell me how to find the intercepts i should be fine with the rest of the question thanks.

I guess you mean you are having trouble finding the critical points, not the intercepts.

You need to find (x,y) that make both ycos(x) and sin(x) = 0. What x make sin(x) = 0? Do any of them make cos(x) = 0? If you use the x's that make sin(x) = 0 is there any way to make ycos(x) = 0? What (x,y) work in both equations?

 

[oceansoft]

I guess you mean you are having trouble finding the critical points, not the intercepts.

You need to find (x,y) that make both ycos(x) and sin(x) = 0. What x make sin(x) = 0? Do any of them make cos(x) = 0? If you use the x's that make sin(x) = 0 is there any way to make ycos(x) = 0? What (x,y) work in both equations?

So u mean like x= 0, pi, 2pi and so on

and then subing those x's into 0=ycos and then solving for y? but if i do it will go on forever beause it says to find all critical points

 

[Char. Limit]

So u mean like x= 0, pi, 2pi and so on

and then subing those x's into 0=ycos and then solving for y? but if i do it will go on forever beause it says to find all critical points

Just say that x=\pi n \forall n \epsilon Z

 

[LCKurtz]

Find and classify all local minima, local maxima and saddle points for the function
f(x,y)=ysin(x)

i can do this question however i am having problem with finding the x and y intercepts i get

fx= ycos(x) and fy=sin(x)
0=ycos(x) and 0=sin(x)

i start to have problem now after someone can tell me how to find the intercepts i should be fine with the rest of the question thanks.

I guess you mean you are having trouble finding the critical points, not the intercepts.

You need to find (x,y) that make both ycos(x) and sin(x) = 0. What x make sin(x) = 0? Do any of them make cos(x) = 0? If you use the x's that make sin(x) = 0 is there any way to make ycos(x) = 0? What (x,y) work in both equations?

So u mean like x= 0, pi, 2pi and so on

and then subing those x's into 0=ycos and then solving for y? but if i do it will go on forever beause it says to find all critical points

Yes, x = n pi make sin(x) = 0. Now answer the next questions I asked:

Do any of them make cos(x) = 0?

If you use the x's that make sin(x) = 0 is there any way to make ycos(x) = 0?

What (x,y) work in both equations?

And, yes, there is nothing wrong with having infinitely many critical points.

 

[oceansoft]

Yes, x = n pi make sin(x) = 0. Now answer the next questions I asked:

Do any of them make cos(x) = 0?

If you use the x's that make sin(x) = 0 is there any way to make ycos(x) = 0?

What (x,y) work in both equations?

And, yes, there is nothing wrong with having infinitely many critical points.

Am not too sure what u are asking but if i sub any of the x's i found using sin(x)=0 into cos(x)=0 i will just get 1 or -1 does that mean that y is always equal to zero?

therefore x= n pi and y=0
btw thanks for ur time

 

[LCKurtz]

Am not too sure what u are asking but if i sub any of the x's i found using sin(x)=0 into cos(x)=0 i will just get 1 or -1 does that mean that y is always equal to zero?

therefore x= n pi and y=0
btw thanks for ur time

Yes, that's exactly it. So your critical points are (n pi, 0).