- Use the first derivative to determine where a function is going up or down, and identify points that might be local highs or lows
- Apply the second derivative to find out where a function curves upward or downward and locate points where this curvature changes
- Use the second derivative test to determine if a point on a graph is the highest or lowest within specific sections
Roller Coaster Calculus: Analyzing Thrills through Functions
In this activity, we will explore the dynamic world of roller coaster physics by analyzing the mathematical model of a roller coaster track’s height as a function of its horizontal distance. Using calculus, we will calculate the first and second derivatives to determine the slope and concavity of the track, identify critical points, and classify extrema and inflection points. This hands-on exercise will enhance your understanding of how mathematical concepts are used to analyze real-world scenarios in engineering and physics.
