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Identify the graph of a function using its first and second derivatives
Free printable Calculus math worksheet for "Identify the graph of a function using its first and second derivatives" — practice analyze functions using the second derivative. No-prep, print or assign online.
This worksheet provides challenging practice for high school calculus students to analyze functions using their first and second derivatives. Teachers can use it to reinforce skills in interpreting derivative graphs, understanding concavity, and connecting derivative behavior to the shape of the original function. It supports deep conceptual understanding of function analysis and graph identification through application-based problems.
Learning objectives
- Interpret the first derivative to determine intervals of increase and decrease in a function's graph
- Analyze the second derivative to identify concavity and points of inflection
- Use first and second derivative information to accurately sketch or identify the graph of a function
Answer Key
How to use this worksheet
- Click “Download Worksheet” and sign in with Google or email to get the PDF instantly.
- Print at home or in class for High School; it's no-prep, with no extra materials needed.
- Use the included answer key to mark it in seconds.
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