<Dl> <Dd> f" (x) = 6 x . (\ displaystyle f' ' (x) = 6x .) </Dd> </Dl> <Dd> f" (x) = 6 x . (\ displaystyle f' ' (x) = 6x .) </Dd> <P> The second derivative of a function f measures the concavity of the graph of f . A function whose second derivative is positive will be concave up (also referred to as convex), meaning that the tangent line will lie below the graph of the function . Similarly, a function whose second derivative is negative will be concave down (also simply called concave), and its tangent lines will lie above the graph of the function . </P> <P> If the second derivative of a function changes sign, the graph of the function will switch from concave down to concave up, or vice versa . A point where this occurs is called an inflection point . Assuming the second derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second derivative is zero is necessarily a point of inflection . </P>

What does it mean if second derivative is negative