S7
Change & Rate
Rate → Derivative
"If you can measure change, you can predict trends."
Philosophical Origin：Newton calculus
Minimal Example
Car travels 60 miles in 2 hours. Speed = 60/2 = 30 mph.
One-Line Rule
"Rate is change per unit."
Common Misconception vs Correct Understanding
Speed is just distance.
Speed is distance per time.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Average rate: Total change / Total time
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Instantaneous rate: Limit as interval approaches 0
如果你能 ↑ 那么你就能 ↓
3
Slope: Rate of change on graph
如果你能 ↑ 那么你就能 ↓
4
Derivative: Instantaneous rate function
如果你能 ↑ 那么你就能 ↓
5
Applications: Velocity, acceleration, growth
SAT Example Question
Question:
If y = x², what is the average rate of change from x=2 to x=4?
Answer:
6
Explanation:
(16-4)/(4-2) = 12/2 = 6
Practice Questions
5 questions with multiple solution methods
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