key term - Changes from negative to positive

Definition

When the graph of the first derivative changes from negative to positive at a certain point, it means that at that point, the original function is transitioning from decreasing to increasing.

Related terms

Local minimum: A local minimum occurs when a function reaches its lowest point within a small interval. At this point, both the first derivative and second derivative test positive.

Inflection point: An inflection point is where a function changes concavity. It can occur when the second derivative equals zero or does not exist.

Increasing function: An increasing function refers to a function whose values increase as the input increases. The first derivative of an increasing function is always positive.