As films are pushed, the higher the rated speed the (more/less?) development needed.
The question is a tad confusing, because strictly speaking when we say that we are going to "push" a film we are using a bit of shorthand. Actually, you don't "push" film, you "push" the film's development.
If you rate the film at a higher speed, it receives less light when you expose it. When you process the film, in order to have the highlights come out dense enough in the negative, you often need to increase (in other words "push") the development.
Usually, we increase development by increasing the time, but increasing temperature or decreasing dilution also works.
You will also end up increasing the contrast too, but unfortunately won't be able to get the same increase of density in the shadows, so most likely some detail will be lost there.
Hope this helps.
As development time increases, the highlights in the negatives will appear darker. There will be a negligible effect on the shadows. There will be a moderate effect on the midtones.
As developer concentration increases, the less dev time needed.
As films are pushed, the higher the rated speed the (more/less?) development needed. Films cannot be successfully pushed. Shadow density is a function of exposure. Increasing development time of underexposed film only increases contrast. Your shadow detail will still be obliterated.
As printing grade increases, the contrast of the print increases.
As print exposure increases, the darker the print.
"darker" is not a precise enough term since it can be construed to apply generally to the entire image. Use density instead and in proper context. The oft-used phrase is "exposure controls density and development controls contrast". If you increase concentration of developer it does allow for a decrease in development time but also may result in uneven development, e.g. due to the time it takes to drain developer from the tank. Agitation is another factor affecting development. It's important to understand the effects of different variables rather than simply being able to regurgitate them on demand. Your next exam might require you to provide a strategy to deal with a particular exposure scenario.