Sign of Derivative and Increasing or Decreasing
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Lesson Summary:
In this lesson, the focus is on understanding the sign of the derivative in relation to the increase or decrease of a function. Using a graph of a cubic function and its derivative, the instructor demonstrates how the sign of the derivative indicates the direction of the function's change. When the derivative is positive, the function is increasing, and when it is negative, the function is decreasing. This is an important concept to grasp and essential to mastering objective 1.11.
Lesson Description:
Given a Cartesian graph of a function be able to determine when the rate of change of that function is increasing and decreasing or has obtained an extrema.
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Questions answered by this video:
- How do you know when the derivative of a function is positive or negative?
- How do you know if a function is increasing or decreasing based on the sign of its derivative at a point?
- What is the relationship between the graph of a function and the graph of its derivative?
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Staff Review
This lesson explains another relationship between a function and its derivative. It explains what is happening on a function when the derivative of the function is positive or negative. There is just one basic idea to this lesson: a function is increasing when its derivative is positive, and it is decreasing when the derivative is negative.
