Increasing & Decreasing Intervals (Practice) - Khan Academy

Overview

• Topic: Increasing and decreasing intervals in calculus.
• Platform: Khan Academy offers a practice section for determining intervals on which a function is increasing or decreasing in the context of AP/College Calculus AB.

Key Concepts

• Understanding how to determine when a function is increasing or decreasing using calculus.
• Application of derivatives to find these intervals.

Lessons and Resources

• Course: AP/College Calculus AB
  • Unit 5: Applying derivatives to analyze functions.
  • Lesson 3: Determining intervals on which a function is increasing or decreasing.

Specific Lessons:

• Finding decreasing interval given the function
  • Video explaining how to identify decreasing intervals from a given function.
• Finding increasing interval given the derivative
  • Video showing how to determine increasing intervals when the derivative is provided.
• Increasing & Decreasing Intervals Practice:
  • An interactive exercise to practice identifying increase/decrease intervals.
• Increasing & Decreasing Intervals Review:
  • A review session to reinforce learning.

Problem Example

• Function: ( h(x) = x^4 - 2x^3 )
• Question: On which intervals is ( h ) increasing?
  • Multiple choice answers provided:
    • (A) ((3, 2, \infty)) only
    • (B) ((-\infty, 3, 2)) only
    • (C) ((-\infty, 0)) and ((32, \infty))
    • (D) ((0, 32)) only
    • (E) The entire domain of ( h )

Additional Resources

• Related Content:
  • Video Tutorial: "Finding decreasing interval given the function" (5:18 minutes)

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