Calculus: Why Increasing Functions Have Positive Derivatives

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

f”(x) = positive

If f(x) is increasing, that means the values of f(x) are getting larger as x is increasing.

In terms of calculus, we can say that the derivative of f(x), or f'(x), is positive. This is because the derivative of a function represents its rate of change at a given point, and if the function is increasing, then that means its rate of change (its slope) is positive.

So, in short, if f(x) is increasing, then f'(x) is positive.

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