Lösung 1.1:5
Aus Online Mathematik Brückenkurs 2
Suppose that the tangent touches the curve at the point y0)
(1) |
If we now write the equation of the tangent as =−2x
(2) |
The condition that the tangent goes through the point y0)
![]() | (3) |
In addition to this, the tangent should also pass through the point (1,1),
![]() | (4) |
Equations (1)-(4) constitute a system of equations in the unknowns
Because we are looking for
Equation (2) gives that
![]() |
With k and m expressed in terms of
(3') |
This equation, together with (1), is a system of equations in
![]() ![]() ![]() ![]() |
Substituting equation (1) into (3') gives us an equation in
![]() |
i.e.
This quadratic equation has solutions
![]() ![]() |
Equation (1) gives the corresponding y-values,
![]() ![]() |
Thus, the answers are the points 2
−3+2
2)
2
−3−2
2)