Stationary points of functions help!!!?

Question

Find and classify the stationary points of the following functions:
z=ysinx

Answer 1

z=ysinx
dz/dx=ycos x=0
dz/dy=sin x=0
y=0 or cosx= 0 x=(2k+1)pi/2 but for this values sinx is not zero
so
y=0 and x= kpi are the critical points
Zxx= -ysinx
Zyy=0
Zxy=cosx
ZxxZyy=Zxy^2= 0-1=-1
All these points are saddle points

Answer 2

The observe "table particular" capacity fastened or unmoved. evaluate the function f(x) = 2x - a million in many cases, we could desire to photograph f(x) in 2 dimensions (x-axis and y-axis). we could desire to additionally think of of f(x) as taking x values and shifting them on the x-axis. as an party f(3) = 2(3) - a million = 6 - a million = 5. because of the fact of this f(x) strikes the three to the 5 (or, indoors the two-dimensonal photograph, strikes the (3, 0) to (5,0) ). As 3 isn't such as 5, x = 3 isn't table particular of f(x). on the comparable time as is f(x) such as x ?

Answer 3

Stationary points in this case are those for which the periodic function touches the x-axis.

x = n(pi)

n is an integer