Increasing, Decreasing & Extrema - Worksheet 1 - 12th Grade
EasyFind increasing/decreasing intervals and local extrema (Easy)
15 problems · 25-30 minutes · Skills: derivatives, analysis, calculus
About This Worksheet
This easy-level worksheet contains 15 problems designed for 12th Grade students practicing increasing, decreasing & extrema. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.
Finding extrema using the first derivative is one of the most practically useful calculus skills — it directly solves optimization problems that arise in business, engineering, and physics. The first derivative test is a systematic, rigorous method for finding the best outcome in any modeled scenario.
- Find critical points by setting the first derivative equal to zero or finding where it is undefined
- Apply the First Derivative Test to classify critical points as local maxima, minima, or neither
- Determine intervals where a function is increasing or decreasing
- Find absolute extrema on a closed interval using the Closed Interval Method
- Locate all local extrema of a polynomial and verify with a sign chart
How to Solve: Worked Example
- Read the problem carefully.
- Identify what is being asked.
- Use what you know to find the answer.
- Check your work.
Answer Key
Frequently Asked Questions
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Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.
How do I find worksheets at different difficulty levels?
Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.
What skills does this applications of derivatives worksheet cover?
This worksheet focuses on derivatives, analysis, calculus. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.
Can I use this worksheet in my classroom?
Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.
How many problems are on this worksheet?
This worksheet contains 15 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.