Study of continuous change through derivatives and integrals.
Derivatives are used everywhere! They help us find where things reach their highest or lowest points, how fast things change, and where curves are steepest or flattest.
Want to build the biggest box from a fixed piece of material? Or minimize fuel costs? Use derivatives to find where the slope is zero—these are your maximum or minimum points.
In physics, velocity is the derivative of position, and acceleration is the derivative of velocity. Derivatives help us model how things move, fall, or speed up.
By analyzing where the derivative is positive, negative, or zero, you can sketch the shape of a function and predict its behavior.
\[f'(a) = 0 \Rightarrow \text{possible max/min at } x = a\]
Finding the minimum cost of materials for a can with a fixed volume.
Determining when a car reaches its top speed by finding where acceleration is zero.
Derivatives help us optimize, analyze motion, and understand the shape of graphs.