I have an object of which I would like to curve one face.
What I have:
What I want to do:
My final goal is to model a television:
My blend file:
How do I curve just one face?
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I would add a few loop cuts (Ctrl+R) and then use proportional editing to pull the middle cut out (from side view), you can change the falloff type to spherical at the bottom of the view to get a more rounded look.
pulling cut out
A different approach (than my other answer) would be to modify the mesh slightly so that you could perform a bevel operation.
Beveling rounds off a corner, so you need a corner where you want the rounded part instead of a flat face. I accomplished this by connecting the two edges across the face and moving the new edge to a positing where it's two adjoining faces are at right angles.
You can then select the new edge and hit Ctrl+B to bevel the edge into a curve, using the mouse wheel to control the number of subdivisions.