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.

More Answers:
Concave Down Functions: The Role Of Second Derivative F”(X)
Concave Up Functions: The Relationship Between Second Derivative And Graph Shape
The Relationship Between Decreasing Functions And Negative Derivatives In Calculus

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