Differential Calculus
Problem M-D-1.6
Difference Quotients and Commmon Tangents of 2 Funktions
Given are the functions
$$ f:x \mapsto f(x) = x^2+1,~D_f = \mathbb{R} $$
and
$$ g:x \mapsto g(x) = -x^2-1,~D_g = \mathbb{R} $$
- Determine the derivatives \(f^\prime\) and \(g^\prime\) as the limit of the difference quotient.
- Provide the common tangents of \(f(x)\) and \(g(x)\).
Problem M-D-1.7
Tangent Line and Normal Line
Determine the points on the graph of
$$ f:x \mapsto f(x) = \frac{1}{x^2},~D_f = \mathbb{R} \setminus \{0\}$$
where the tangent line is also the normal line for the same curve. (The normal line is the perpendicular line to the tangent at the point of contact.)
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