When f ‘(x) is positive, f(x) is
When f ‘(x) is positive, it means that the derivative of the function f(x) with respect to x is positive
When f ‘(x) is positive, it means that the derivative of the function f(x) with respect to x is positive. The derivative of a function represents the rate of change of the function at any given point.
If f ‘(x) is positive, it implies that the function f(x) is increasing. This means that as x increases, the value of f(x) also increases. In other words, the function is growing or getting larger.
For example, consider the function f(x) = x^2. The derivative of f(x) is f ‘(x) = 2x. When x > 0, the derivative is positive, indicating that the function is increasing. As x increases, the value of f(x) also increases. Similarly, when x < 0, the derivative is negative, indicating that the function is decreasing. As x decreases, the value of f(x) decreases. In summary, when f '(x) is positive, it means that the slope or rate of change of the function f(x) is positive, which implies that the function is increasing.
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