Recent content by copacetic

  1. C

    Minimum distance of functions in a metric space

    Woops! You're right, I had x*e^x instead of x*e^x-e^x. Well that got rid of the nasty e now I'm left with t=3/2. Thanks!
  2. C

    Minimum distance of functions in a metric space

    Ok thanks, in the end I have \frac{2}{3}t - 2e + 1 = 0 t = 3e - \frac{3}{2}
  3. C

    Minimum distance of functions in a metric space

    I would need to find the first derivative, find the roots and then check their sign in the second derivative. Can I do this without the square root around the entire function? Because with it the derivative is enormous and I'm not sure how I'd go about solving it for 0.
  4. C

    Minimum distance of functions in a metric space

    Homework Statement A metric on C[0,1] is defined by: d(f,g) = ( \int_0^1 \! (f(x) - g_t(x))^2 \, dx )^{1/2} Find t e R such that the distance between the functions f(x) = e^x - 1 and g_t(x) = t * x is minimal. Homework Equations Given above The Attempt at a Solution The first...