For the graph of [math] shown below, sketch two functions [math] with [math]. In one let [math]; in the other, let [math]. Mark [math], [math] and [math] on the [math]-axis of your graph. Identify local maxima, minima and inflection points of [math].

(a) At which point does [math] achieve its largest value?



(b) At which point does [math] achieve its smallest value?



For the following questions, consider only the interior points on the domain on which [math] is shown.
(c) How many critical points does [math] have?





(d) How many local maxima does [math] have?





(e) How many local minima does [math] have?





(f) How many inflection points does [math] have?