Increasing, Decreasing & Extrema Worksheet 10

Use derivative signs and stated geometric constraints to interpret functions and rates.

hard: Use another set to practice explaining and checking your answers.

23 problems · 25-30 minutes · Skills: derivatives, analysis, calculus

About This Worksheet

This hard-level worksheet contains 23 problems designed for 12th Grade students practicing increasing, decreasing & extrema. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

Use derivative signs and stated geometric constraints to interpret functions and rates.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: For f(x) = 3(x - 3)² - 2, find the intervals of increase and decrease and the minimum.

Solution Steps:

f′(x) = 6(x - 3).
The derivative is negative left of h and positive right of h.

Answer: Decreasing on (−∞, 3); increasing on (3, ∞). Minimum at (3, -2).

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

For f(x) = 2(x + 3)² + 2, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x + 5)² - 4, find the intervals of increase and decrease and the minimum.

For f(x) = 4(x - 3)² + 1, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x + 2)² + 1, find the intervals of increase and decrease and the minimum.

For f(x) = 3(x + 1)² - 2, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x + 3)² + 0, find the intervals of increase and decrease and the minimum.

For f(x) = 3(x + 0)² - 1, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x + 4)² + 5, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x - 2)² + 5, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x - 1)² - 2, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x - 1)² - 5, find the intervals of increase and decrease and the minimum.

For f(x) = 3(x - 5)² + 4, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x + 1)² + 5, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x - 1)² + 5, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x + 1)² - 4, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x + 5)² + 4, find the intervals of increase and decrease and the minimum.

For f(x) = 2(x + 5)² - 5, find the intervals of increase and decrease and the minimum.

For f(x) = 5(x + 1)² - 3, find the intervals of increase and decrease and the minimum.

For f(x) = 6(x - 2)² - 5, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x + 4)² + 5, find the intervals of increase and decrease and the minimum.

For f(x) = 4(x + 1)² - 4, find the intervals of increase and decrease and the minimum.

For f(x) = 1(x - 2)² + 4, find the intervals of increase and decrease and the minimum.

For f(x) = 4(x + 4)² + 5, find the intervals of increase and decrease and the minimum.

Answer Key

1. Decreasing on (−∞, -3); increasing on (-3, ∞). Minimum at (-3, 2).2. Decreasing on (−∞, -5); increasing on (-5, ∞). Minimum at (-5, -4).3. Decreasing on (−∞, 3); increasing on (3, ∞). Minimum at (3, 1).4. Decreasing on (−∞, -2); increasing on (-2, ∞). Minimum at (-2, 1).5. Decreasing on (−∞, -1); increasing on (-1, ∞). Minimum at (-1, -2).6. Decreasing on (−∞, -3); increasing on (-3, ∞). Minimum at (-3, 0).7. Decreasing on (−∞, 0); increasing on (0, ∞). Minimum at (0, -1).8. Decreasing on (−∞, -4); increasing on (-4, ∞). Minimum at (-4, 5).9. Decreasing on (−∞, 2); increasing on (2, ∞). Minimum at (2, 5).10. Decreasing on (−∞, 1); increasing on (1, ∞). Minimum at (1, -2).11. Decreasing on (−∞, 1); increasing on (1, ∞). Minimum at (1, -5).12. Decreasing on (−∞, 5); increasing on (5, ∞). Minimum at (5, 4).13. Decreasing on (−∞, -1); increasing on (-1, ∞). Minimum at (-1, 5).14. Decreasing on (−∞, 1); increasing on (1, ∞). Minimum at (1, 5).15. Decreasing on (−∞, -1); increasing on (-1, ∞). Minimum at (-1, -4).16. Decreasing on (−∞, -5); increasing on (-5, ∞). Minimum at (-5, 4).17. Decreasing on (−∞, -5); increasing on (-5, ∞). Minimum at (-5, -5).18. Decreasing on (−∞, -1); increasing on (-1, ∞). Minimum at (-1, -3).19. Decreasing on (−∞, 2); increasing on (2, ∞). Minimum at (2, -5).20. Decreasing on (−∞, -4); increasing on (-4, ∞). Minimum at (-4, 5).21. Decreasing on (−∞, -1); increasing on (-1, ∞). Minimum at (-1, -4).22. Decreasing on (−∞, 2); increasing on (2, ∞). Minimum at (2, 4).23. Decreasing on (−∞, -4); increasing on (-4, ∞). Minimum at (-4, 5).

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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.

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This worksheet contains 23 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.