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.
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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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.