Differentiate the following functions.
Here you see the graph of the function .
The graph seems to be decreasing for every value of except . Prove that this is indeed the case.
The tangent to the graph of for intersects the -axis in the point . Calculate the coordinates of .
Find the derivatives of the following functions:
Here you see the graph of the function .
Determine the domain of .
Algebraically compute the range of .
Denote the edgepoints of the graph of by and . For what value of is the slope of the tangent to the graph equal to that of the line ?
A water line needs to be laid from point A to point C. Along the street the cost is € 30,00 per meter and though the field € 70,00 per meter. The length of is meter and the length of is meter. There are several ways to lay the water line:
along the street to point and then through the bordering terrain to point ;
directly from through the field, in a straight line to ;
or in one of many ways in between: the line then is laid partly along the street to point , and then from the street to point .
What is the cost if you choose the first option?
What is the cost if you choose the second option?
Study the third option. Denote the length of by the variable . Now express the cost voor the laying of this water line in .
How should the water line be laid to minimize the cost? Calculate the minimal cost using the derivative.