Functions of Two Variables. Need Help

[iylia]

I need some help with one of my tutorial questions. This is the question
http://img122.imageshack.us/img122/9820/ques3dd3.jpg

For Part (a), I have found the partial derivatives as

Fx (x,y) = Cos(x) Sin(y)
Fy (x,y) = Sin(x) Cos (y)

Then to find the stationary points, Let Fx = 0 and Fy = 0. But I am not sure how to find the values..

For Part (b), I have no idea how to solve it..

For Part (c), I know the chain rule for two variables but I am not sure how to apply it to this question. If someone could point out an example that would be great =)

Thx for the help!

 

[malawi_glenn]

(a)Fx = 0 when x = 0 or y = pi/2, or x = pi or y = 3pi/2 etc. as long as you are confined within the domain.

(b) hint: gradient of function is the normal vector of the function surface at a certain point.

chain rule is
dg/dt = (df/dx)(dx/dt) + (df/dy)(dy/dt)

were x = t^2; y = exp(t)

if then f(x,y) is Sin(x) * Sin(y)

we get:

df/dx = Cos(t^2) Sin(exp(t))

and (df/dx)*(dx/dt) = 2tCos(t^2) Sin(exp(t))

similar for (df/dy)(dy/dt)

but I am not so sure about the chain rule anymore.