Understanding the relationship between the increasing derivative and positive second derivative: Explained

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

If the derivative of a function, f'(x), is increasing, it means that the slope of the function at any given point is also increasing

If the derivative of a function, f'(x), is increasing, it means that the slope of the function at any given point is also increasing. In other words, as we move along the x-axis, the rate at which the function is changing is increasing.

Now, let’s consider the second derivative of the function, f”(x). The second derivative represents the rate at which the slope of the original function is changing. If the second derivative is positive, it means that the slope of the function is increasing. If the second derivative is negative, it means that the slope of the function is decreasing.

So, based on the fact that f'(x) is increasing, we can conclude that f”(x) is positive. This means that the rate at which the slope of the function is changing is positive, or in other words, the function is becoming steeper as we move along the x-axis.

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