What does f" say about f? Definition: Let f be differentiable on (a, b). The graph of a function, f, is concave upward on the interval (a, b) if f (x) is increasing on (a, b). (If the graph of f lies above all of its tangents on an interval (a, b)) The graph of a function, f, is concave downward on the interval (a, b) if f'(x) is decreasing on (a, b). (If the graph of f lies below all of its tangents on an interval (a, b))Concavity Test (a). If f"(x) > 0 for all x in (a, b), then f is concave upward on (a, b). (b). If f"(x)