Find mins and maxes y' = xsin(x) - cos(x)

[nitro_nay]

Ok, the question gives me the derivative of an equation, which is y' = xsin(x) - cos(x). How would I find the mins and maxes (aka, find the roots of 0 = xsin(x) - cos(x)). I've tried finding an equivalent fnction, which resulted in a page of work telling me 0 = 1, so I'm lost now. Any help would be appreciated

 

[arthur ohlsten]

y'= x sin x - cosx
set y'=0
cosx =x sinx
x= cosx/sinx
x=cot x

let us plot y=x
a straight line slope 1

let us plot y= cot x
a curve of period pi, with amplitude -oo<y<oo

the curves cross an infinite number of times with a infinite number of critical points.

I hopev this helps.
I suggest you find the point between 0<x<pi/2 as one solution.

Arthur