An Excursion through Elementary Mathematics, Volume I by Antonio Caminha Muniz Neto

Author:Antonio Caminha Muniz Neto
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In Fig. 9.9, points x 0, x 0 ′ and x 0 ′ ′ are of local minimum for the function f: (a, b) → ℝ whose graph is depicted. Observe that, in a neighborhood of each of these points, the values of f are no less than those it assumes at x 0, x 0 ′ and x 0 ′ ′ (as indicated by the three dashed horizontal line segments). Also, x 0 ′ is the only global minimum point of f (i.e., a point in which f attains the minimum possible value in (a, b)), whereas x 0 and x 0 ′ ′ are not global minimum points. Finally, notice that f has also two maximum local points (identify them!), albeit none of which is a global maximum point.

Fig. 9.9Local minimum points of

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