Tangent Line to a Curve

The tangent line to a curve is a fundamental concept in calculus and analytic geometry, providing insight into the behavior of functions at specific points. It represents a straight line that touches the curve at a single point, mirroring the curve's slope at that precise location. Understanding tangent lines enables mathematicians and scientists to approximate curves, analyze rates of change, and solve various real-world problems. This concept serves as a cornerstone in calculus, facilitating deeper comprehension of functions, derivatives, and their applications in fields ranging from physics to economics.