What is the best way to solve these tasks?
Rectangles are examined where two sides lie on the coordinate axes and one vertex lies on the function graph in the 1st quadrant.
- Determine the rectangles with the maximum area.
- Determine the rectangles with the minimum perimeter.
Hello, my dears,
What's the best way to solve this? I'm really not making any progress. Thanks in advance ❤️
It is known that the area content of rectangles is calculated by multiplying the two side lengths with one another.
Here, the side width has the length t and the side height corresponds to the functional value, i.e. f(t). That is, the “area function” is: A(t)=t * f(t).
Use the corresponding terms, optionally multiply and then determine the maximum from A.
The procedure at the maximum extent is to set up the same “entry function” and then determine the maximum thereof.
Thanks first, but I’m just stupid in math. Maybe you could finish. I’d be very grateful to you. Only if you want to, but otherwise very dear of you
You have the corner (t, f(t)). If this is the corner, how long are the sides of the rectangle?
How large is the area of the right corner as a function of t?
A(t) = ….
How large is the circumference of the rectangle as a function of t?
U(t) = …
How to determine the maximum and the minimum?
Thanks first, but I’m just stupid in math. Maybe you could finish. I’d be very grateful to you. Only if you want to, but otherwise very dear of you
Set up target function and condition.
To set the target function with only one variable.
Investigate this function on Extrema.
(Such tasks do not fall from heaven)