Question

Найдите точку минимума функции y=(13-x)e^(13-x)

Answer 1

$y=(13-x)e^{13-x}\\y'=-e^{13-x}-(13-x)e^{13-x}=e^{13-x}cdot (x-14)=0\\e^{13-x} textgreater 0; ,; x-14=0; ; to ; ; x=14\\Znaki; y':; ; ---(14)+++\\x_{min}=14\\y_{min}=(13-14)e^{-1}=-frac{1}{e}\\Tochka; ; (14;-frac{1}{e}).$