Let’s say the speed limit is 40mph.
If you wanted to conserve gas, would it make more sense to speed up quickly to about 50 and let your car coast down to about 35 before speeding up to 50 again and doing the same thing over and over, or would it make more sense to lay on the gas and stay at a constant 40mph?
I get the best MPG at a steady pace; pushing the pedal uses more fuel. At least according to the display on my dashboard.
Of course…
…YMMV!
(Couldn’t resist.)
You might search for “duty cycles” to investigate this further. I dimly remember the term from the '70s.
Another term to look at is “engine braking.” It is supposedly better speed up and then coast, although it has a drawback of severely pissing off the people behind you. Constant acceleration may be less efficient, and in that case it is probably better to use cruise control if you have it.
OK< I searched on duty cycle now what? 
Cite? Any time you have braking engine or wheel (it makes no difference), you are wasting fuel. Hybrids with re-gen braking don’t count. 
Anytime you brake energy that you extracted out of your gas is being used for something other than propelling the car. In the case of wheel brakes it is turned into heat and wear on your brakes. In the case of engine braking you are doing work to turn the engine against compression. To get the best gas mileage, you want to use as much of the energy from the gas for movement as possible, not wasting it by braking.
As far as speeding up past your target speed and coasting, besides the engine braking issue, you have to contend with wind resistance. Wind resistance is not linear.
Different usage, I guess. “Duty cycle” was the term used for the phenomenon called “engine braking” by thelurkinghorror.
Actually, when a hybrid brakes, it’s wasting fuel, too, just not as much. But even with a hybrid, it helps to avoid unnecessary braking.
We have a lot of hills around where I live and I’ve been experimenting with drifting down them in neutural. Like one small town I go through I get drift almost all the way. And coming to my house I can drift the last 1.5 miles or so to my driveway.
By doing this I can get 350 miles on a tank of gas. Normally I get around 300-315. Maybe I’m just driving more carefully when I’m trying the drifting, but either way I’m saving a couple gallons of gas.