The Relationship Between an Increasing Function and Its Derivative: Explained

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

If f(x) is an increasing function, it means that as x increases, the corresponding values of f(x) also increase

If f(x) is an increasing function, it means that as x increases, the corresponding values of f(x) also increase. This implies that the rate of change of f(x) with respect to x, which is given by f'(x) (the derivative of f(x) with respect to x), should be greater than zero.

Therefore, if f(x) is increasing, then f'(x) > 0. In other words, the derivative of an increasing function f(x) is positive.

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