When f ‘(x) is positive, f(x) is
When the derivative of a function f'(x) is positive, it means that the function f(x) is increasing
When the derivative of a function f'(x) is positive, it means that the function f(x) is increasing. In other words, as x increases, the corresponding values of f(x) also increase.
To understand this concept better, let’s consider an example. Suppose we have a function f(x) that represents the position of an object at a given time. The derivative f'(x) represents the velocity of the object at that time.
If f'(x) is positive, it means that the object is moving in the positive direction. As time increases (x increases), the position of the object also increases. This indicates that the object is moving forward or upward, depending on the context of the problem.
Similarly, in general mathematics, when the derivative of a function is positive, it implies that the function is increasing. This holds true for various types of functions, including polynomials, exponential functions, and trigonometric functions.
To summarize, when f'(x) is positive, it tells us that the function f(x) is increasing, and the corresponding values of f(x) increase as x increases.
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