Find the derivative of the following functions:
Given is the function .
Algebraically find the extrema of .
Calculate the slope of the graph of for .
Algebraically calculate the coördinates of the inflection point of the graph of .
The point lies on the graph of the function .
Calculate the slope of the tangent of the graph in this point.
In how many other points does the tangent have the same slope?
A piece of cardboard of by centimeters is folded into a tray. Assume that the height of the tray is cm.
The volume of this tray only depends on (if nothing is allowed to stick out above the edge). Compose a fitting function rule for the volume .
Algebraically calculate what value of gives the maximum volume for the tray.
Here you see a part of the graph of .
In the visible part of the graph there are three points in which the tangent to the graph is parallell to the -axis. Algebraically calculate the -coordinates of those three points.
Why does the function have only two (local) extrema?