Why A Negative Derivative Indicates Decreasing Math Functions

When f ‘(x) is negative, f(x) is

decreasing

When the derivative f ‘(x) is negative, it means that the function f(x) is decreasing.

Intuitively, this means that as you move along the x-axis from left to right, the values of f(x) are getting smaller. This can be seen graphically as a downward slope.

For example, let’s say we have the function f(x) = -x² + 3x + 2. If we take its derivative, we get f ‘(x) = -2x + 3. When f ‘(x) is negative (i.e. when -2x + 3 < 0), we can solve for x to get x > 3/2. This tells us that the function f(x) is decreasing for x > 3/2.

So, when f ‘(x) is negative, we can conclude that f(x) is decreasing at that point.

More Answers:
Increasing F'(X): How It Affects Steepness And Rate Of Change In F(X)
Discovering Local Maximums In Math: The Relationship Between Derivatives And Function Peaks.
Local Minimum In Math: How A Change In Slope Indicates A Transition From Decreasing To Increasing Trend

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »