Ask me some practice questions about critical numbers in increasing and decreasing functions.
Understand the Problem
The question is requesting practice problems related to determining critical numbers in the context of increasing and decreasing functions. This involves analyzing a function's derivative to identify intervals where the function is increasing or decreasing.
Answer
1. Find the critical points of f(x) = 3x^3 - 9x^2 + 6x. 2. Determine intervals of increase/decrease for f(x) = x^4 - 4x^2. 3. Find relative extrema using first derivative test f(x) = e^x - x. 4. Find critical points for f(x) = ln(x).
Here are some practice questions:
- Find the critical points of the function f(x) = 3x^3 - 9x^2 + 6x.
- Determine the intervals on which the function f(x) = x^4 - 4x^2 is increasing or decreasing.
- Use the first derivative test to find the relative extrema of the function f(x) = e^x - x.
- For the function f(x) = ln(x), find the critical points and determine the concavity.
Answer for screen readers
Here are some practice questions:
- Find the critical points of the function f(x) = 3x^3 - 9x^2 + 6x.
- Determine the intervals on which the function f(x) = x^4 - 4x^2 is increasing or decreasing.
- Use the first derivative test to find the relative extrema of the function f(x) = e^x - x.
- For the function f(x) = ln(x), find the critical points and determine the concavity.
More Information
These practice problems involve finding critical points, determining intervals of increase and decrease, and applying the first derivative test to identify relative extrema. Such problems are important for understanding the behavior of functions and their graphs.
Tips
A common mistake is not correctly calculating the derivative or setting it equal to zero incorrectly when finding critical points. Always double-check your calculations.
Sources
- Calculus I - Critical Points (Practice Problems) - tutorial.math.lamar.edu
- Finding Critical Numbers, Intervals of Increasing/Decreasing, and ... - youtube.com
AI-generated content may contain errors. Please verify critical information
