EDB — 1TD

Exercises

1. [1TD]Prerequisites:[14W]↺↻.Note:written exam, June 23th, 2012.

   Let f be a \(C^ 1\) class function on \(ℝ\), with \(f (0) ≠ 0\). Prove that \(x ∈ ℝ\) exists such that the two vectors

   \[ v = (x, f (x)) \quad , \quad w = (− f' (x), 1) \]

   are linearly dependent. (Note that the vector \(w\) is orthogonal to the tangent of the graph of \(f\).) Discuss the possibility that this condition is verified for every \(x ∈ ℝ\).

   Solution 1

   [1TF]↺↻