Question

найти точку минимума f(x)=(x-1)^2 x+2

Answer 1

f(x)=(x-1)^2/(x+2)

f`(x)=(2(x-1)(x+2)-(x-1)^2)/((x+2)^2=

       =(2(x^2+x-2)-(x^2-2x+1))/((x+2)^2=

      =(x^2+4x-5)/((x+2)^2=(x-1)(x+5)/((x+2)^2

 

   +                -                 -                  +

---------[-5]-------(-2)------------[1]-----------

          max         перегиб         min

 

Xmin=1