Hi there guys!

this one's interesting but got me stumped.

 

How would i show that the values of x at which sinxe^(-sinx) has stationary points form an arithmetic sequence?

 

Thanks!

i assume you meant [sinx][exp(-sinx)]. just do the most obvious thing which is to find its derivative.

 

which comes out to be

 

[cosx]exp[-sinx] - [sinx][cosx]exp[-sinx]. to find the stationary points , find points such that the derivative at the point is zero. so setting that to 0 we get

 

[cosx]exp[-sinx] - [sinx][cosx]exp[-sinx] = 0

 

iff cosx - sinx[cosx] = 0 as the exponential is never 0.

 

so we have either cosx = 0 or sinx = 1

 

which gives just the same arithmetic sequence of solutions namely

 

(pi/2 + n*pi), where n ranges over the integers.

thanks for your help!