convexupward

convexupward is a term used to describe the shape of a curve or function that bends upwards, like a bowl or a smiley face. Mathematically, a function is convex upward on an interval if its second derivative is non-negative over that interval. This means that the slope of the tangent line to the curve is increasing as you move from left to right. Another way to characterize a convex upward function is that the line segment connecting any two points on the graph of the function lies above or on the graph itself. Examples of functions that are convex upward include quadratic functions of the form y = ax^2 + bx + c where 'a' is positive, and exponential functions like y = e^x. Understanding convexity is important in various fields, including optimization, economics, and physics, as it helps in analyzing the behavior of functions and finding minimum or maximum values.