Photos are printed on rectangular sheets of paper of m2 to make posters. Around a picture the edge remains white: at the bottom edge a strip
of dm wide, at the other edges strips of dm wide.
What dimensions of the poster maximize the printed area?
Make a sketch of this situation with the data added.
Try to solve the problem by yourself first. Only look at c and d if you don't succeed.
Assume that the width of a poster is denoted by dm. Derive a formula for the area of the printed part as a function of .
Using differentiation calculate the value of for which is maximal.
Now answer the question asked in the beginning.
Somebody wants to buy a ladder to clean his gutters. Next to his house at a distance of m from the wall there is a fence with a height of m.
How tall should the ladder at least be so that it can be placed against the wall of
the house over the fence?
(Assume that both the wall and the fence are perpendicular to the ground.)
How long are the edges of the isosceles triangle with the greatest area and a circumference of cm?
Look at the graph of function with on the domain . The line (with ) intersects the -axis in point and the graph of in point .
Show that the area of rectangle is equal to: .
Use differentiation to determine what maximizes the area of rectangle .
Given the family of functions where .
Algebarically calculate the extrema of when .
For what values of does not have extrema?
For what values of does the tangent to the graph of at have a slope of ?
In a Cartesian coordinate system line with intersects the graph of in point .
Calculate the minimal possible length line segment can have.
Now assume that . Line intersects the -axis in and rectangle has points and on the graph of and point also lies on the -axis.
Calculate the maximum value for rectangle .