Introduction to Derivatives
Derivatives are a fundamental tool in calculus used to study how functions change. They represent the rate at which a function's output value is changing at any given point.
The Formal Definition
The derivative of a function f at a point a is defined as:
Practical Applications
Understanding derivatives allows us to model and solve real-world problems involving rates of change. 📈 Whether it's calculating the velocity of an object or predicting stock market trends, derivatives are crucial!
Interesting Problem
Consider the position function of a frog jumping along a straight line: s(t) = 5t^2 + 3t + 8. What is the velocity of the frog at time t seconds?
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