Gas Pumping and Swimming Velocity Analysis

In the gas station scene, f(t) is the flow rate of gasoline in gallons per second, and f(t) dt represents the total gallons pumped over time. Skibidi vibes hit as we use a right Riemann sum to estimate the flow from 60 to 135 seconds. We lowkey know there must be a c where f'(c) equals the average rate, thanks to the Mean Value Theorem, so that is sigma logic. Switching to Stephen's swim game, his velocity is wild, oscillating like a goon in the pool. We can ship these calculations to find the average flow and rate of change, keeping it dank and on the edge of calculus mastery.