driving on hilly roads

You don't need to be concerned about stressing the engine. Just change the oil regularly. The automatic transmission will select the correct gear. Just push the gas pedal as far as you need, including all the way down to the floor. To conserve gas, just push the gas pedal smoothly and anticipate your moves. If there's no one behind you, and you have time, you can go slower. Running the engine harder doesn't harm an engine in good condition. The maximum torque is just over 4,000 rpm and the maximum horsepower just over 5,000 rpm, and the redline just over 6,000 rpm, so running the engine up over 3,000 rpm is just fine. You get better mileage in higher gears (numerically lower), best mileage in overdrive with the lockup clutch engaged. You can tell when you're in overdrive with the torque converter lock up engaged by looking at the relation between the tachometer and the speedometer. When the tach needle moves up under acceleration, and the road speed is about the same, the torque converter unlocked. You may get better mileage by reaching the base of those hills at higher speed (if conditions permit) so you can stay in the higher gear. If the hill is steep enough that when you press the gas to keep going, the transmission downshifts, that's fine. As long as the engine is warmed up when you're doing this, just maintain the necessary road speed as needed. With computer controlled fuel injection, the correct amount of fuel is metered automatically so you're only going to use what's needed. If you were in a fuel mileage competition, you would gradually build speed on the flats and let the speed bleed off on the hills, coming just short of a complete stop at the top and then building speed again downhill. But if you're on the road with other drivers, just maintain the speed limit and let the car automatically select the right gear. Stressing the engine is really no problem, can be good to wind it out. Stress on the engine comes from neglecting oil changes, where localized hot spots are created, or letting the ignition components deteriorate such that incomplete combustion occurs, or neglecting cooling system maintenance so the engine runs hotter than should be. Stessing the transmission comes from running old, dirty, discolored, contaminated fluid and overheating the transmission by using it to "hold" the car on a hill by slipping constantly. Another wonderful way to destroy a transmission is to let the car roll in Reverse, and then shift to Drive before stopping completely. Stated in the affirmative: always come to a _complete_ stop before changing direction and shifting gears.

Daniel,

Thanks for the excellent points.