Understanding the Relationship between Increasing f'(x) and Positive f”(x) in Functions

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 increasing

If f'(x) is increasing, it means that the derivative of the function f(x) is increasing. The derivative represents the rate of change of the function.

Now, let’s consider the second derivative, f”(x), which represents the rate of change of the derivative. If f'(x) is increasing, it means that the rate of change of f(x) is itself increasing.

This implies that f”(x) is positive. When f”(x) is positive, it indicates that the slope of the derivative is increasing. In other words, the rate of change of the rate of change is increasing.

Therefore, if f'(x) is increasing, then f”(x) must be positive.

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