If f(x) is decreasing, then f'(x) is?
If a function f(x) is decreasing, it means that as the value of x increases, the value of f(x) decreases
If a function f(x) is decreasing, it means that as the value of x increases, the value of f(x) decreases.
The derivative of a function, denoted as f'(x) or dy/dx, represents the rate of change of the function with respect to x. In other words, it tells us how fast the function is changing at a given point.
To determine the relationship between the decreasing behavior of f(x) and the derivative f'(x), we need to understand how the signs of f(x) and f'(x) are related.
If f(x) is decreasing, it means that as x increases, f(x) is getting smaller. This implies that the slope of the function is negative.
Now, the slope of a function at a specific point is given by the value of its derivative at that point. If f(x) is decreasing, it means that the slope (i.e., the derivative) is negative.
Therefore, we can conclude that if f(x) is decreasing, then f'(x) is negative.
More Answers:
Calculating the Average Rate of Change of a Function on an Interval: A Step-by-Step Guide with Example Calculation for f(x) = 2x + 3Understanding the Instantaneous Rate of Change at a Specific Point: A Guide to Calculating the Derivative and Analyzing Function Behavior
Understanding the Relationship between Increasing Functions and Positive Derivatives in Mathematics.