Найти точку минимума.
y=(x-2)^2*e^х-6

у = (x–2)2·ex–6

y'=((х – 2)2)'·еx–6+(х – 2)2·(еx–6)'=2(x–2)·(x–2)'·ex–6+(x–2)2·ex–6·(x–6)'=2(x–2)·ex–6+(x–2)2·ex–6=ex–6·(x–2)·(2+x–2)=ex–6·(x–2)·x

ex–6·(x–2)·x=0

x=2 и х=0 – стационарные точки.