Lösung 1.3:4
Aus Online Mathematik Brückenkurs 2
If we call the
FIGURE
The area of the rectangle is then given by
x
=
1−x2
and we will try to choose
To begin with, we note that, because
0
0
1
x
x
1
There are three types of points which can maximise the area function:
1. critical points, 2. points where the function is not differentiable, 3. endpoints of the region of definition.
The function
x
=x
1−x2
0
=A
1
=0
We must therefore supposed that the maximum area is a critical point. We differentiate
x
=1
1−x2
+x
−2x
=1−3x2
and the condition that the derivative should be zero gives that
1
3
3
x
1
1
3
=−6
1
3
0
which shows that
3
The answer is that the point
1
3
1−
1
3
2
=
1
3
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