There is not a management VLAN per se on Cisco switches. There are VLANs (layer 2 broadcast domains) which may or may not have layer 3 Switched Virtual Interfaces (SVIs) active on the switch. Any active SVI (or routed port) may be used to manage the switch. Some folks use an SVI on vlan 1 for management. To chane that see below.
The 3750X also has an Ethernet management port that is assigned to a separate VRF (VLAN Routing and Forwardng instance - think of it as a separate routing table). If you are using that port for management (optional), it is configured like any other interface.
Depending on whether you switch is layer 2 only (lanbase license) or has routing enabled (ipbase or ipservices license), changing the switch IP address may need to change either the ip default gateway (layer 2 switch), default route (layer 3 switch without a dynamic routing protocol), or routing process (layer 3 swith cwith dynamic routing protocol) settings.
We can best answer your question definitively if you share the output of the following commands from the CLI:
show ip int br | ex una
show run int fa0
If you use the VLAN 1 layer 3 address scheme, here is how you would change it from the CLI (assuming you have enable login mode established) using an example address of 192.168.1.5 on a /24 subnet with a gateway of 192.168.1.1:
ip address 192.168.1.5 255.255.255.0
ip default-gateway 192.168.1.1
wr mem (or copy run start)
This needs to be done with care and preferably from console since if it is the only address on the switch, you will lose access as soon as you change the IP address. If you were logged in via the GUI or even via a vty line, you would lose and be unable to re-establish the connection (from off that local subnet anyhow).
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