Changes from Positive to Negative

Definition

When the first derivative of a function changes from positive to negative at a specific point, it means that the slope of the function is decreasing as we move towards that point.

Related terms

Local Maximum:

A local maximum occurs when a function reaches its highest value in a particular interval but may not be the absolute maximum over its entire domain.

Inflection Point:

An inflection point is where the concavity of a curve changes. It occurs when the second derivative changes sign.

Critical Point:

A critical point is where either the first derivative does not exist or is zero. It can correspond to local extrema or points of inflection.