Let be defined by for and .
Show that f has an absolute minimum at , but that its derivative has both positive and negative values in every neighborhood of 0 .
Let be defined by for and .
Show that f has an absolute minimum at , but that its derivative has both positive and negative values in every neighborhood of 0 .
. Thus, . The fact that let's you draw the proper conclusion.
Now, . Notice that and so it suffices to show the claim for
Now, choose values of small enough to fit into any range such that the first two terms are irrelevant.