Curve Sketching Worksheet/Game

Curve Sketching Worksheet/Game
Welcome to Curve Sketching Worksheet/Game. This game is an interactive calculus drill designed to sharpen your ability to analyze functions using derivatives. It tests your knowledge of increasing/decreasing intervals, local extrema, and concavity. Scroll down the page for a more detailed explanation.

 

 

How to play the Curve Sketching Worksheet/Game
The game presents you with a series of mathematical functions and asks specific analytical questions based on calculus principles. This will help you to graph functions using derivatives.

1. Analysis Topics
   You will be asked to identify:
   Increasing/Decreasing Intervals: Where the first derivative f’(x) is positive or negative.
   Local Extrema: The x-values for local maximums and minimums (where f’(x) = 0).
   Concavity: Where the second derivative f’’(x) is positive (concave up) or negative (concave down).
   Inflection Points: Where the concavity changes (where f’’(x) = 0).
   

2. Scoring & Levels
   Question Bank: Each session consists of 15 randomized levels pulled from a pool of polynomial, exponential, and trigonometric functions.
   Progress Tracking: The top bar shows your current level and your running score (Correct / Total Attempts.
   

How to Play
Step 1: Start the Drill
Click “Start Drill” from the main menu. The first level will load immediately.

Step 2: Solve the Prompt
Read the function at the top of the card (e.g., f(x) = x^2 - 6x) and the specific question below it (e.g., “Where is f(x) increasing?”).
Tip: Mentally calculate the derivative. For x^2 - 6x, the derivative is 2x - 6. It is increasing when 2x - 6 > 0, so x > 3.

Step 3: Choose Your Answer
Click one of the multiple-choice buttons in the grid.
Correct: The button turns Emerald Green, a high-pitched success chime plays, and you’ll see the message “Analyzed!"
Incorrect: The button turns Red, a low-pitched error sound plays, and the correct answer is highlighted in green for your reference.

Step 4: Advance
Click “Next Question” to proceed. You cannot change your answer once a button is clicked.

Step 5: Review Your Rank
After 15 questions, you will receive your final accuracy percentage and a title based on your skill.

Quick Reference Table

Feature	Condition to Look For
Increasing	f’(x) > 0
Decreasing	f’(x) < 0
Concave Up	f’’(x) > 0
Concave Down	f’’(x) < 0
Local Max/Min	f’(x) = 0 (and check sign change)

Curve Sketching - Graphing Functions Using Derivatives

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