Final answer:
The DHCP client uses the broadcast address 255.255.255.255 as the destination IP address in its DHCP discover message to reach all available DHCP servers on the local network.
Step-by-step explanation:
When a DHCP client sends a DHCP discover message, it creates an IP datagram with a special destination IP address. Since the client does not have an IP address at this point, the destination IP address used is the broadcast address, which is 255.255.255.255. This broadcast address is used so that all DHCP servers on the local network segment can receive the discover message. The DHCP discover message is the client's way of asking if there are any DHCP servers available that can assign it an IP address. The use of the broadcast address ensures that the client's request is heard by any listening DHCP server on the network, allowing the server to respond with a DHCP offer.