Increasing and Decreasing Functions - Calculus

TL;DR

Learn how to determine when a function is increasing and decreasing using the first derivative and sign charts.

Transcript

in this video we're going to focus on finding the intervals where a function is increasing and when it's decreasing so let's say if you have a graph anytime the graph is going upward if it's going up then the function is increasing the first derivative is positive now if the graph is going down it can be going down in many different ways when it's ... Read More

Key Insights

• ❓ A function is increasing when the first derivative is positive, indicating a positive slope.
• ❎ A function is decreasing when the first derivative is negative, indicating a negative slope.
• 📈 Sign charts can be used to determine the intervals of increase and decrease without graphing the function.
• 📈 Absolute value functions can be analyzed by comparing the inside part of the function to zero and graphing the resulting transformation.
• ☺️ Critical numbers of a function are values of x where the first derivative is zero or undefined.
• 😥 Test points within intervals can be used to evaluate the sign of the first derivative and determine if the function is increasing or decreasing.
• 🤬 Intervals of increase and decrease are written using inequality symbols with infinity as appropriate.

Summary & Key Takeaways

• The video explains how to find intervals of function increase and decrease without graphing the function by finding the first derivative, setting it equal to zero, and creating a sign chart.

• It provides examples of finding intervals for different functions, such as f(x) = x^2 - 3x + 1 and f(x) = x^3 - 9x^2 + 24x.

• The video also demonstrates how to analyze absolute value functions and determine their intervals of increase and decrease.