Derivatives, representing instantaneous rates of change, find extensive applications across diverse fields. In physics, they model velocity and acceleration, crucial for analyzing motion. Economics leverages derivatives to optimize profit, understand marginal cost and revenue, and predict market trends. Engineering utilizes them in designing optimal structures, analyzing fluid dynamics, and modeling heat transfer. In computer science, derivatives aid in optimization algorithms and machine learning. Furthermore, derivatives are integral to solving complex equations and approximating functions in numerous scientific and engineering problems. Their applications extend to medicine (modeling drug diffusion), and finance (risk management and option pricing), demonstrating their versatility in analyzing change and optimizing systems.
What is the derivative of f(x) = x³ at x = 2?
Which application does NOT directly utilize derivatives?
In simple terms, what does the derivative of a function at a point represent?