Recent content by christos.miko

  1. C

    Is there a differentiable function that satisfies these conditions?

    Is there a function f , differentiable for all real x, such that | f (x) |< 2 and f (x)f ′ (x) ≥ sin(x)? I noticed that [f(x)*f(x)]' = 2f(x)*f'(x) = [f(x)]^2 So I tried multiplying that inequality by 2. 2f (x)f ′ (x) ≥ 2sin(x) Then I tried integrating both sides. [f(x)]^2 ≥...
  2. C

    Really difficult calculus problem

    Is there a function f , differentiable for all real x, such that | f (x) |< 2 and f (x)f ′ (x) ≥ sin(x)?I noticed that [f(x)*f(x)]' = 2f(x)*f'(x) = [f(x)]^2 So I tried multiplying that inequality by 2. 2f (x)f ′ (x) ≥ 2sin(x) Then I tried integrating both sides. [f(x)]^2 ≥ -2cos(x). This...