The Relationship Between Decreasing Functions And Derivatives – Explained By A Math Expert

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

f”(x) = negative

If f(x) is a decreasing function, it means that as the input variable x increases, the output values of the function f(x) decrease. In other words, the slope of the tangent line to the graph of f(x) is negative for all points on the function.

Now, the derivative f'(x) represents the slope of the tangent line to the graph of f(x) at any given point x. If the function is decreasing, then the slope of the tangent line is negative, meaning that f'(x) is negative for all values of x.

Therefore, we can conclude that if f(x) is decreasing, then f'(x) is negative.

More Answers:
The Relationship Between Increasing F'(X) And Positive F”(X) – Exploring The Concave Up Graph Of F(X)
Concave Down Functions: Relationship Between F(X) Graph And F”(X)
Concavity In Math: Positive Second Derivative And Curved Functions

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