Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Lösung 1.3:1a

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 1.3:1a moved to Solution 1.3:1a: Robot: moved page)
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
+
A critical point is a point where the derivative is equal to zero, i.e. the function has a horizontal tangent. For the function in the exercise, this occurs when
-
<center> [[Image:1_3_1a-1(2).gif]] </center>
+
<math>\text{x}=0</math>.
-
{{NAVCONTENT_STOP}}
+
 
-
{{NAVCONTENT_START}}
+
 
-
<center> [[Image:1_3_1a-2(2).gif]] </center>
+
-
{{NAVCONTENT_STOP}}
+
-
[[Image:1_3_1_a1.gif|center]]
 
[[Image:1_3_1_a2.gif|center]]
[[Image:1_3_1_a2.gif|center]]
 +
 +
In addition, the point at the origin is a local and global minimum, because no other points give a smaller value for the function that the point at
 +
<math>\text{x}=0</math>. On the other hand, there are no inflexion points (points where the derivative is both zero and has the same sign on both sides of the point).
 +
 +
To the left of
 +
<math>\text{x}=0</math>, the derivative is negative (the tangent slopes downwards) and the function is strictly decreasing, and to the right of
 +
<math>\text{x}=0</math>
 +
the derivative ) the tangent slopes upwards) and the function is strictly increasing.
[[Image:1_3_1_a3.gif|center]]
[[Image:1_3_1_a3.gif|center]]

Version vom 08:58, 15. Okt. 2008

A critical point is a point where the derivative is equal to zero, i.e. the function has a horizontal tangent. For the function in the exercise, this occurs when x=0.



In addition, the point at the origin is a local and global minimum, because no other points give a smaller value for the function that the point at x=0. On the other hand, there are no inflexion points (points where the derivative is both zero and has the same sign on both sides of the point).

To the left of x=0, the derivative is negative (the tangent slopes downwards) and the function is strictly decreasing, and to the right of x=0 the derivative ) the tangent slopes upwards) and the function is strictly increasing.

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.3:1a“