Question

Multivariable Calculus

Answer 1

I know the formula for the saddle point but I don't know how to find the maximums or minimums.

Answer 2

The maxima, minima, and saddle points constitute all the points where our derivatives all vanish i.e. the tangent plane is horizontal and parallel to the \(xy\)-plane

Answer 3

$$f(x,y)=\sin x\sin y\\f_x(x,y)=\cos x\sin y\\f_y(x,y)=\sin x\cos y$$We want all the solutions to both$$\cos x\sin y=0\\\sin x\cos y=0$$We know that if, say, \(\cos x=0\) then \(\sin x=1\) (to satisfy the Pythagoran identity) so we know that only one out of each pairs \(\cos x,\sin x\) and \(\cos y,\sin y\) can be \(0\) at a time.

Answer 4

Hence we require that either \(\cos x=\cos y=0\) or \(\sin y=\sin x=0\)

Answer 5

Ohh. I did not know this >.> .

Answer 6

well, visualize it! :-)