Find the derivative of the following functions.
Here you see the graphs of the functions and . The function is the product function of both.
The zeroes of can be deduced from the graph. What are the zeroes of the graph of ?
Show that
Use the derivative to find th extrema of .
For what values of does the equation have exactly four solutions?
Given is the function .
For what values of does the graph have a tangent parallell to the -axis?
This function has two extrema. What are they?
Here you see the graph of the function the way the graphing calculator depicts it.
The graph is incomplete. You can tell this from the zeroes of this function. What zeroes does the graph of have?
Calculate the range of using differentiation .
Compose the equation for the tangent to the graph of in .
Given is the function .
Algebraically calculate the range of .
Calculate the coordinates of the inflection point of the graph of .
For what is the line with equation a tangent to the graph of ?
Somebody wishes to expand his house with a conservatory using four equally sized rectangular frames. The dimensions of each fo these frames are: height and width . He first studies the possible arrangements where two frames and are attached perpendicular to the wall. The other two frames and are placed in such a manner that the area of the floor is maximized.
The distance between two frames perpendicular to the wall is . Show that the area of the floor of the conservatory corresponds to: .
Algebraically calculate the maximum floor area for this conservatory.