duction (Read This First!) Given ( ) () x a A x f t dt = , recall that Ax fx () () = by the Fundamental Theorem of Calculus Part I. This means that A x( ) is an antiderivative of f x( ) along with the initial condition A a() 0 = . Recall from Calculus I the relationships between a function and its derivative (such as "When a function is increasing, its derivative is positive). Using those same relationships, we have: A x( ) is increasing when f x( ) is positive. A x( ) is decreasing when f x( ) is negative. A x( ) has a local maximum when f x( ) changes from positive to negative. A x( ) has a local minimum when f x( ) changes from negative to positive. A x( ) is concave up when f x( ) is increasing. A x( ) is concave down when f x( ) is decreasing. A x( ) has an inflection point when f x( ) changes direction (incr to decr or decr to incr)