The Relationship Between Increasing f'(x) and Positive f”(x)

If f'(x) is increasing, then f”(x) is?

If f'(x) is increasing, it means that the derivative of the function f(x) is also increasing across its domain

If f'(x) is increasing, it means that the derivative of the function f(x) is also increasing across its domain. In other words, as x increases, the rate at which f(x) is changing also increases.

Now, let’s consider the second derivative of the function, which is denoted as f”(x). The second derivative represents the rate at which the derivative of f(x) is changing. In simpler terms, it describes how the slope of the tangent line to the graph of f(x) is changing.

If f'(x) is increasing, this means that the slope of the tangent line to the graph of f(x) is increasing as well. In other words, as x increases, the slope of the tangent line is becoming steeper.

Therefore, if f'(x) is increasing, it indicates that the rate at which the slope of the tangent line to the graph of f(x) is changing (i.e., f”(x)) is positive. In mathematical terms, f”(x) > 0.

So, if f'(x) is increasing, then f”(x) is a positive value.

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