
27 P.3d 562 (2001)
2001 UT App 87
STATE of Utah, in the interest of A.G., S.G., and L.G., persons under eighteen years of age.
R.G. and K.G., Appellants,
v.
State of Utah, Appellee.
No. 20000052-CA.
Court of Appeals of Utah.
March 15, 2001.
*563 April Freedman, Salt Lake City, for Appellants.
Mark L. Shurtleff, Atty. Gen., and John Peterson, Salt Lake City, for Appellee.
Martha Pierce and Susan Eisenman, Salt Lake City, Guardians Ad Litem.
Before Judges JACKSON, BENCH, and BILLINGS.

OPINION
BENCH, Judge:
¶ 1 Appellants appeal the juvenile court's order terminating their parental rights with respect to A.G., S.G., and L.G., as well as the juvenile court's denials of Appellants' post-judgment motions for relief from the order and for amended judgment. We affirm.
¶ 2 Parents may file a petition to voluntarily relinquish their parental rights to a child. See Utah Code Ann. § 78-3a-407(7) (1996). Because relinquishment is irrevocable, the court must: 1) certify that the relinquishing parent has "read and understands the . . . relinquishment [petition] and has signed it freely and voluntarily," and 2) determine that relinquishment is in the child's best interest. Utah Code Ann. §§ 78-3a-414(2), (4) (1996 & Supp.2000).
¶ 3 Appellants challenge the adequacy of the protections afforded a parent in section 78-3a-414. In comparing a parent relinquishing parental rights to a criminal pleading guilty, Appellants contend that due process requires juvenile courts to strictly comply with the requirements of Rule 11 of the Utah Rules of Criminal Procedure before accepting a parent's relinquishment petition and ordering termination of parental rights. Appellants do not cite any direct legal authority for applying Rule 11, a rule of criminal procedure, to the civil matter of voluntary relinquishment of parental rights.[1] Moreover, the United States Supreme Court has recognized that parents facing termination of their parental rights are not entitled to the same level of due process protection afforded criminal defendants. See Lassiter v. Department of Soc. Serv., 452 U.S. 18, 32, 101 S.Ct. 2153, 2162, 68 L.Ed.2d 640 (1981). Thus, while we recognize that parents have a "commanding" legal interest in their children, id. at 27, 101 S.Ct. at 2160, compliance with Rule 11 is simply not required in a civil case where parents voluntarily relinquish their parental rights.
¶ 4 We now turn to the issue of whether the relinquishment proceeding in the present case complied with section 78-3a-414. The juvenile court's findings of fact indicate that Appellants understood the consequences of signing the relinquishment petition, understood the permanent nature of those consequences, and signed the petition freely and voluntarily. See Utah Code Ann. § 78-3a-414(2). We uphold these findings of fact unless they are "clearly erroneous," meaning that they are against the "clear weight of the evidence." In re S.L., 1999 UT App 390, ¶20, 995 P.2d 17 (citations omitted).
¶ 5 The clear weight of evidence here shows that Appellants understood what relinquishment meant. Before signing the petition, they each acknowledged that they had read the petition and understood its terms. In fact, Appellants each acknowledged that *564 they had reviewed the document with counsel prior to the hearing. At the hearing, Appellants were each asked about and acknowledged understanding the individual provisions of the petition. The mother specifically acknowledged understanding that she would have "no further rights regarding the future care, custody or control of [the] children," and that she would "have no right regarding notification of what's going on with the children, whether they're adopted or what else happens with them." Likewise, the father acknowledged understanding that he was relinquishing "all the obligations, guardianship, custody, control, [and] responsibility of the three children," and that he would have no say in who adopted the children.
¶ 6 After acknowledging the permanent nature of their decision to relinquish all rights to their children, Appellants each freely and voluntarily signed a relinquishment petition. The mother acknowledged understanding that relinquishment was an "irrevocable act," and the father acknowledged understanding that unless the relinquishment met one of the limited appeal standards, his parental rights "would be permanently terminated." In addition, both acknowledged that after signing the document, they could not change their minds. When given the opportunity, neither parent asked any questions. Then, after answering a series of questions to affirm that they were mentally sound, not under the influence of any medication or controlled substance, and had not been coerced or promised anything in exchange for their signatures, Appellants each signed a petition.
¶ 7 The juvenile court must also determine that termination of parental rights is in the children's best interests. See Utah Code Ann. § 78-3a-414(4). This determination is a legal conclusion,[2] which we review for abuse of discretion. See In re S.L., 995 P.2d 17, 1999 UT App 390 at ¶32. Appellants argue that when asked whether they felt termination of parental rights was in the children's best interests, their answers indicate only that they felt termination was best at the present time, but that they were working out their problems and hoped to be able to provide for the children in the future. Following those equivocal answers, follow-up questions revealed that resolving the mother's problems would take a "significant amount of time," and that the father felt the children "deserve a lot more than I can give them right now." Then, Appellants both unequivocally agreed that relinquishment and adoption into a loving and stable environment was in the children's best interests. Given this testimony, the family's extensive history with the Division of Child and Family Services, and the nature of Appellants' personal problems, we conclude that the juvenile court did not abuse its discretion in determining that termination of parental rights was in the children's best interests.
¶ 8 Appellants finally assert that they were denied effective assistance of counsel. In their briefs on appeal, Appellants' only argument on this issue is a terse assertion, without citation to the record or any legal authority, that counsels' "superficial and cursory examination of [Appellants]" constituted ineffective assistance of counsel because it prevented them from both expressing their true feelings and demonstrating "on record that [they] had an adequate understanding" of the proceeding and its consequences. Rule 24(9) of the Utah Rules of Appellate Procedure requires that all arguments contain "citations to the authorities, statutes, and parts of the record relied on." Id. Because Appellants have failed to cite to the record and any legal authority in support of their ineffective assistance claim, we could properly refuse to consider it. See State v. Thomas, 1999 UT 2, ¶ 11, 974 P.2d 269.
¶ 9 In any event, the argument fails on its merits. Appellants first raised their ineffective assistance claim in their post-judgment motion under Rule 60(b)(6) of the Utah Rules of Civil Procedure.[3] To establish a claim for ineffective assistance of counsel, an appellant must show that "counsel's performance was objectively deficient and that counsel's deficient performance prejudiced *565 the case." In re E.H., 880 P.2d 11, 13 (Utah Ct.App.1994). Appellants' only contention in their briefs on appeal is that counsels' examinations of Appellants during the relinquishment proceeding were inadequate. Even assuming that counsels' examinations were objectively deficient, Appellants were not prejudiced. The record establishes that the requirements of section 78-3a-414 were met. In addition, Appellants were given an opportunity to ask questions at the hearing, and they were asked to explain in their own words why termination of parental rights and adoption was in the children's best interests. Thus, the juvenile court did not abuse its discretion in denying Appellants' Rule 60(b) motion. See Franklin Covey Client Sales, Inc. v. Melvin, 2000 UT App 110, ¶ 9, 2 P.3d 451 (establishing abuse of discretion as the proper standard of review for denial of Rule 60(b) motions).
¶ 10 We affirm the juvenile court's orders terminating Appellants' parental rights and denying their post-judgment motions.
¶ 11 WE CONCUR: NORMAN H. JACKSON, Associate Presiding Judge, JUDITH M. BILLINGS, Judge.
NOTES
[1]  At oral argument, Appellants cited In re D.L.S., 112 Wis.2d 180, 332 N.W.2d 293 (1983). The court in In re D.L.S., however, merely applied the Wisconsin statutory requirements for voluntary relinquishment of parental rights, which include an explicit right to a jury trial if requested by the relinquishing parent. See id. at 296 n. 5. In re D.L.S. does not stand for the proposition that due process requires a court to comply with Rule 11 in voluntary relinquishment cases.
[2]  Although a conclusion on the best interest of the children is included in the juvenile court's findings of fact, such a determination is "more properly labeled a conclusion of law." In re S.L., 995 P.2d 17, 1999 UT App 390 at ¶ 30 n. 6.
[3]  Rule 60(b)(6) is "sufficiently broad" to permit a court to set aside a judgment for ineffective assistance of counsel. Stewart v. Sullivan, 29 Utah 2d 156, 158, 506 P.2d 74, 76 (1973).
