Lösung 1.1:4
Aus Online Mathematik Brückenkurs 2
If we write the equation of the tangent as
we know that the tangent's slope k is equal to the derivative of =2x
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We can determine the constant m with the condition that the tangent should go through the grazing point (1,1), i.e. the point (1,1) should satisfy the equation of the tangent
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which gives that
The normal to the curve
Because two straight lines which are perpendicular to each other have slopes which satisfy k2=−1
The equation of the normal can therefore be written as
where n is some constant.
Since the normal must pass through the line (1,1), we can determine the constant n if we substitute the point into the equation of the normal,
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and this gives