Calculus › Using derivatives › concave down
concave down
Using derivatives
A function is described as concave down on an interval if its second derivative is negative, indicating that the first derivative is decreasing, and thus the slope of the tangent line to the function is decreasing. In such cases, the tangent line to the function lies above the curve throughout the interval.
Applications
This condition is characterized by a negative second derivative, which implies that the first derivative is decreasing, and the tangent lines to the curve lie above the curve itself.