Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
A positive derivative refers to the rate at which a function is increasing. When the derivative of a function is positive, it means that the slope of the function is positive and the graph is getting steeper as x increases.
A negative derivative indicates that the function is decreasing. This would be like stepping on the brake pedal while driving uphill, causing your speed to decrease.
Zero Derivative: A zero derivative means that there is no change in slope or direction. It's like cruising along a flat road where neither acceleration nor deceleration occurs.
An inflection point occurs when the concavity of a curve changes from convex to concave (or vice versa). It can be thought of as reaching the top or bottom of a hill before starting to descend or ascend again.