What is Calculus?
Calculus is the study of continuous change. It helps us understand motion, growth, and optimization in fields like physics, engineering, and economics.
Visual representation of a function's curve showing starting and ending points.
Basic Concepts
- Limits: Understanding function behavior
- Derivatives: Measuring instantaneous rate of change
- Integrals: Calculating accumulated quantities
Derivatives in Action
Derivatives help us find slopes of curves at specific points. Here's how it works in real-world applications:
Derivative Formula
Derivative of $ f(x) = x^2 $:
[ f'(x) = \lim_{h \to 0} \frac{(x+h)^2 - x^2}{h} = 2x ]
// Example in JavaScript:
function derivative(f, x) {
const h = 0.0001;
return (f(x + h) - f(x)) / h;
}
function powerFunction(x) { return x * x; }
console.log(derivative(powerFunction, 3); // Should print ≈6
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