if f'(x) is EQUAL to 0, then f is _____ on (a,b)
If f'(x) is equal to 0, this means that the derivative of the function f(x) is equal to zero
If f'(x) is equal to 0, this means that the derivative of the function f(x) is equal to zero. In terms of the behavior of the function f(x), when its derivative is 0 on an interval (a, b), it indicates that the graph of the function has a horizontal tangent line at one or more points within that interval.
In other words, if f'(x) = 0 for some values of x in the interval (a, b), it means that the function f(x) is neither increasing nor decreasing at those particular x-values. This implies that the function may have a local extreme point (a maximum or minimum) at those x-values.
To summarize, when f'(x) is equal to 0 on the interval (a, b), the function f(x) may have local maximum or minimum points at those specific x-values. However, it does not necessarily mean that the function f(x) is constant on the entire interval.
More Answers:
Understanding Intervals of Increase and Decrease | Analyzing Math Functions Based on x-Values or the DomainUnderstanding Increasing Functions | The Relationship between f'(x) and the Increase in f(x)
Understanding Decreasing Functions | The Relationship Between f'(x) and f(x)