MA130 Calculus 1 Take-home Assessment 6C Name: 1. You start pedaling your (single-gear) bike. The number times you pedal a full rotation in t seconds since starting is p(t). The function w(p) takes a number of pedal rotations and produces how many wheel rotations have occurred. Explain why the chain-rule formula dw dw dp dt dp dt calculates how quickly the number of wheel rotations is changing over time. Do not simply "cancel" dp, I want an intuitive physical explanation. 2. Explain why the product rule formula (fg)' = f'g+ g's is true. If you follow the explanation from class, make sure to explain why the f'g' term disappears. You are also welcome to research other explanations online, just don't copy anything word-for-word. Note that I do not want a mathematical proof, but an intuitive explanation