Slew rate is the rate of change of output voltage.
i.e., when a step input is applied, in how much time the output reaching the input in buffer configuration.
slew rate is inversely proportional to settling time. If settling time is more, slew rate is less. If the time to settle the output voltage is less, the slew rate is more.
High bandwidth is required to settle down for systems having high settling time. For systems having low settling time, have low bandwidth to accomodate.
i.e., bandwidth is directly proportional to settling time. and settling time is inversely proportional to slew rate.
so, ultimately bandwidthis inversely proportioal to slew rate.