To meet the requirement of fault tolerance when one interface goes down, BIG-IP must use link aggregation so that loss of a single physical link does not isolate the VLAN(s).
How the objects relate (data plane view)
Interfaces = physical links.
Trunk (LACP) = bundles multiple interfaces into one logical link that provides redundancy (and possibly bandwidth aggregation).
VLANs are assigned to interfaces or trunks. If you need multiple VLANs on the same trunk, they must use 802.1Q tagging (because you can only have one untagged VLAN per interface/trunk).
Self IPs are then placed on the VLANs to provide BIG-IP presence and routing/ARP functions, but self IPs are not what provides link resiliency—the trunk does.
Why Option D is correct
You have two physical interfaces and you want resiliency if one fails → put both interfaces into one trunk with LACP enabled.
You need both external and internal VLANs on those same two links → both VLANs should be configured as tagged on that trunk, so they can coexist on the same aggregated link.
If either physical interface fails, the trunk remains up via the remaining interface, keeping both VLANs operational.
Why the other options are incorrect
A: Two VLANs cannot both be untagged on the same trunk/interface. Only one untagged VLAN is possible; additional VLANs must be tagged.
B: Two trunks “each with one VLAN” would typically mean splitting VLANs across separate trunks. With only two interfaces total, that becomes one interface per trunk—if one interface goes down, the VLAN on that interface is down (no redundancy for that VLAN).
C: Same redundancy problem as B, and disabling LACP removes the negotiated aggregation behavior expected when the switch engineer specifically requested LACP.
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