How to find the location of extreme points?

Hi,
I have a function (see attached file).  How can I find by Maple 
those values of beta and f for which W will have 
three consecutive local extrema between the
phi=0 and phi_0 where W=dW/dphi=0 at phi=0 and W=0 at phi_0 and W<0 for 0<abs(phi)<phi_0?
Thanks,
plot.mw