if f'(x) is LESS than 0, then f is _____ on (a,b)
If f'(x) is less than 0, it means that the derivative of the function f(x) is negative
If f'(x) is less than 0, it means that the derivative of the function f(x) is negative. This tells us that the function is decreasing on the interval (a, b).
To understand this concept, it is important to understand the relationship between the derivative and the original function. The derivative represents the rate of change of the function at any given point. When the derivative is negative (less than 0), it means that the function is decreasing, i.e., the function values are decreasing as x increases.
In the context of the interval (a, b), it means that as x moves from a to b, the function values of f decrease. However, this does not necessarily mean that the function is decreasing for all values of x. It specifically refers to the interval (a, b).
To summarize, if f'(x) is less than 0, then f is decreasing on the interval (a, b).
More Answers:
Understanding Rightward Shifting Functions | How Graphs Move to the Right as x IncreasesUnderstanding Intervals of Increase and Decrease | Analyzing Math Functions Based on x-Values or the Domain
Understanding Increasing Functions | The Relationship between f'(x) and the Increase in f(x)