Aus Online Mathematik Brückenkurs 2

Diese Aktion ist beschränkt auf Benutzer, die einer der Gruppen „Administratoren, approved“ angehören.

Quelltext dieser Seite:

There are two points, <math>x=a</math> and <math>x=b</math> (see picture below), where the function has a horizontal tangent and hence a derivative equal to zero. These are the functions critical points. [[Image:1_3_1_b1.gif|center]] Furthermore, we see that the function has local minimum points at the left endpoint of the interval of definition and <math>x=b</math>, because the function takes higher values at neighbouring points. In the same way, we see that the function has local maximum points at <math>x=a</math> and at the right endpoint of the interval of definition. Of these local extreme points, the left endpoint is a global minimum (that point where the function takes its absolute minimum value) and the right endpoint is a global maximum. [[Image:1_3_1_b2.gif|center]] The function is strictly increasing (it has a tangent that slopes upwards) in the interval between the left endpoint and <math>x=a</math>, as well as between <math>x=b</math> and the right endpoint. In the interval between <math>x=0</math> and <math>x=b</math>, the function is strictly decreasing. [[Image:1_3_1_b3.gif|center]]

• 1.3.1b - Solution - The graph with horizontal tangents
• 1.3.1b - Solution - The graph with max's and min's labeled
• 1.3.1b - Solution - The graph with the interval where the function is decreasing
• 1.3.1b - Solution - The graph with the interval where the function is increasing

Zurück zur Seite Hauptseite.