Western Governors University (WGU) MATH1200 C957 Applied Algebra Practice Exam

A concave up function is characterized by the property that its second derivative is positive, implying that as you move along the curve from left to right, the slope of the tangent line to the function is increasing. This means that if you take any two points on the function and draw a line segment between them, the portion of the curve between those two points lies below that line segment, suggesting that the function "opens upward." In this context, the option indicating that the function increases over certain intervals captures the essence of a concave up function. While a concave up function may not always be increasing throughout its entire domain (it can also decrease), there will be intervals where the function indeed increases, leading to the overall tilted shape that characterizes concavity. This understanding highlights how concavity and the behavior of a function's slope are interconnected. By grasping the properties associated with concave up functions, you can better analyze function behavior through critical points, intervals of increase or decrease, and overall trends.