Maxima and minima of functions of two variables

[Mdhiggenz]

Homework Statement

Locate all relative maxima, relative minima ,and saddle points if any.

f(x,y)=ysinx

fx(x,y)=ycosx

fy(x,y)=sinx

ycosx=0 sinx=0
y=0 x=0,∏,2∏... up until infinity
Critical points at (0,0),(∏,0),(2∏,0)...

fxx(x,y)=-ysinx

fyy(x,y)= cosx

fxx*fyy-f(x,y)²→0-0=0 ∴ no relative extrema,

however the book says that fxx*fyy-f(x,y)²=-1 which means saddle point.

I don't understand if y is = to zero.. the function ysinx will always be zero..

Homework Equations

The Attempt at a Solution

 

[hedipaldi]

Fyy=0

 

[Mdhiggenz]

Sorry that was a typo, but still doesn't help regardless.

 

[SammyS]

Homework Statement

Locate all relative maxima, relative minima ,and saddle points if any.

f(x,y)=ysinx

fx(x,y)=ycosx

fy(x,y)=sinx

ycosx=0 sinx=0
y=0 x=0,∏,2∏... up until infinity
Critical points at (0,0),(∏,0),(2∏,0)...

fxx(x,y)=-ysinx

fyy(x,y)= cosx

fxx*fyy-f(x,y)²→0-0=0 ∴ no relative extrema,

however the book says that fxx*fyy-f(x,y)²=-1 which means saddle point.

I don't understand if y is = to zero.. the function ysinx will always be zero..

Homework Equations

The Attempt at a Solution

Isn't f_y(x,y) = sin(x) ?

Then what is f_yy(x,y) ? Isn't it zero?

Also, What is f_xy(x,y) ?

You need fxx*fyy-(fxy)² , not fxx*fyy-f(x,y)²