Follow the slope
What speed uses the least fuel?
Crawl along and the engine burns fuel going nowhere. Race along and the air pushes back hard. Somewhere in between is the speed that uses the least fuel per kilometre. Where?
Your tools. The slope of a curve is how much it rises or falls when you nudge the input a tiny bit. We measure it by asking the fuel formula for its value just left and just right of a speed, and comparing. A negative slope means the curve is still falling: better answers lie to the right.
Investigate. Start with a guess of 40 km/h. Measure the slope there. Take a small step in the downhill direction. Measure again. Repeat sixty times. This is exactly how a machine learning model learns — it follows the slope of its error downhill.
The reveal. The red dots are the guesses. Watch them stride fast where the curve is steep, then bunch up and stop where it flattens. Flat slope means nothing left to gain.
This case is part of the Family plan
Unlock every 12–15 case and the full AI, machine-learning, and deep-learning path — one subscription for the whole family.
Need a hint?
Change the starting guess to 140 and run again — the dots now walk downhill from the other side and stop in the same place.