Your privacy choices

KiwiBee uses optional Google Analytics, Google Ads, and Meta Pixel cookies to understand adult visitors, measure completed sign-ups, and improve campaigns. Essential cookies always stay on. OpenAI’s ChatGPT Ads Pixel also measures page views and completed enquiries after advertising consent, and may use hashed contact details for matching. Privacy policy

Skip to main content

Identify the graph of a function using its first and second derivatives

Printable PDFScroll to explore
Identify the graph of a function using its first and second derivatives — free printable Calculus math worksheet

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

How to use this worksheet

  1. Select “Sign in / Sign up to download”, then sign in with Google or email to get the PDF from KiwiBee Printables.
  2. Print at home or in class for High School; it's no-prep, with no extra materials needed.
  3. Use the included answer key to mark it in seconds.

Good for

ClassworkHomeworkWarm-upCentersSmall groups

Answer Key

Answer key for Identify the graph of a function using its first and second derivatives — free printable Math worksheet

More worksheets like this

Likes & comments

See what other teachers think and share a helpful note.

Loading likes and comments…
Worksheet Studio

Need a different version? Make your own.

Generate a fresh worksheet for any grade, topic and language. Free.

Open Worksheet Studio