When f ‘(x) is negative, f(x) is
When f ‘(x) is negative, it means that the derivative of the function f(x) with respect to x is negative
When f ‘(x) is negative, it means that the derivative of the function f(x) with respect to x is negative. The derivative represents the rate of change of the function.
If f ‘(x) is negative, it implies that the function f(x) is decreasing in the given interval. In other words, as x increases, f(x) becomes smaller. This can be visualized as a downward slope on a graph of f(x).
For example, let’s consider the function f(x) = x^2. The derivative of f(x) is f ‘(x) = 2x. When x is negative, the derivative is negative (e.g., f ‘(-1) = 2(-1) = -2), indicating that the function is decreasing. As x becomes more negative, the value of f(x) becomes smaller.
Similarly, if f ‘(x) is negative for a certain interval, it means that f(x) is decreasing within that interval. This information is useful for understanding the behavior of functions and solving various mathematical problems, such as finding maximum or minimum points and analyzing rates of change.
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