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
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- 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.
Frequently asked questions
Is the “Identify the graph of a function using its first and second derivatives” worksheet free?
Yes. “Identify the graph of a function using its first and second derivatives” is a free printable Math worksheet. Sign in with a free KiwiBee account to download the PDF — it includes up to 25 downloads a month.
What grade or age is this Math worksheet for?
It's designed for High School (ages 14–18), covering Analyze functions using the second derivative.
Does it come with an answer key?
Yes — a matching answer key is included so you can grade it in seconds.
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