In this activity, students will discuss the graphical and algebraic relationships between a function and its first and second derivatives, namely a profit function.

• Students will further discuss the graphical and algebraic relationships between a function and its first and second derivatives, namely a profit function.
• Students will use their knowledge of Optimization to maximize profits or minimize losses.
• Students will use Integration to find a profit function given its rate of change.
•  Students will try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.

• Cost
• Revenue
• Optimization
• Profit
• Differentiation
• Integration

The goal of this activity is to help students understand how the use of derivatives, optimization, and integration affect cost, revenue, and profit equations used in industry from around the world. Students will ultimately try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.