concavity
Concavity describes the direction in which a function curves, determined by the sign of its second derivative. A function is concave up if its second derivative is positive, indicating that the slope of the tangent line is increasing, while a function is concave down if its second derivative is negative, indicating that the slope of the tangent line is decreasing.
Applications
Concavity is a property of a function that describes the direction in which the function curves, determined by the behavior of its first derivative. A function is concave up on an interval if its derivative is increasing, which means the slopes of the tangent lines to the function increase as one moves from left to right, and the tangent lines lie below the curve. Conversely, a function is concave down on an interval if its derivative is decreasing, indicating that the slopes of the tangent lines decrease as one moves from left to right, and the tangent lines lie above the curve.