!
SUBROUTINE findextreme(i, nmax, rvals, vp, jval, rext, v0, v1, v2, root, mu, ichanl)
USE Numeric_Kinds_Module
!-------------------------------------------------------------------------
!this subroutine finds maximum/minimum of the potential function
!-------------------------------------------------------------------------
IMPLICIT none
LOGICAL  :: root
INTEGER  :: i, nmax, jval, ichanl
REAL(dp) :: rext, r1, r2, vl, vr, v0, v1, v2,mu
REAL(dp) :: rvals(nmax), vp(nmax)

 root=.false.
!==============================================================================
! Checks if the first derivative of the potential has changed signs and begins 
!   to home in on exact value of maximum/minimum
 IF(vp(i-1)*vp(i).lt.0.d0)THEN
 r1=rvals(i-1)       !sets initial inner bound to previous r value
       vl=vp(i-1)
       r2=rvals(i)         !sets initial outer bound to current r value
       vr=vp(i)
       ! findext will further narrow down bounds
       CALL findext(rext, v0, v1, v2, r1, vl, r2, vr, jval, mu, ichanl)
       root=.true. !signals that a critical point has been found
    ENDIF

    RETURN
    END SUBROUTINE FindExtreme