What Can You Do With Derivatives?

Derivatives are more than just math—they help solve real-world problems!

• Finding Maxima and Minima: Find highest and lowest points (think: rollercoaster peaks!).
• Optimization: Make things as efficient as possible (like minimizing cost or maximizing area).
• Motion: Describe velocity and acceleration.
• Related Rates: Understand how two or more related quantities change together.

How Are They Used?

• In business, to maximize profit.
• In engineering, to design safer vehicles.
• In biology, to model population changes.

How to Apply Derivatives

1. Set the derivative = 0 to find stationary points.
2. Use the second derivative to check if they’re maxima or minima.
3. Interpret your results in the real-world context.