Is this function: exp ⁡ ( − | | A x | | 2 ) concave in A??

Question

Is this function:  exp  ⁡            (        −      |        |    A  x      |              |        2              )      concave in   A??

Patrick Arnold · Accepted Answer

Let   f  (  x  )  =      e          −              x        2            Then       f    ′    (  x  )  =  −  2  x      e          −              x        2            , so       f    ″    (  x  )  =  4      x    2        e          −              x        2              −  2      e          −              x        2              =  (  4      x    2    −  2  )      e          −              x        2                  e          −              x        2              is always positive, but   4      x    2    −  2 can be positive or negative.

Is this function: exp(−||Ax||^2) concave in A??

Answered question

Answer & Explanation

New Questions in Calculus 1