Question

$y = (9 - x){e}^{x + 9}$
найдите точку максимума функции​

Answer 1

$y=(9-x)e^{x+9}\\\\y'=-e^{x+9}+(9-x)e^{x+9}=e^{x+9}\cdot (-1+9-x)=e^{x+9}\cdot (8-x)=0\\\\e^{x+9}>0\; \; pri\; \; x\in R\; \; \; \Rightarrow \; \; \; 8-x=0\; ,\; x=8\\\\znaki\; y'\, :\; \; +++(8)---\\\\x_{max}=8\; \; ,\; \; y_{max}=(9-8)\cdot e^{17}=e^{17}\\\\Tochka\; max\; :\; \; A(8\, ;\, e^{17})\; .$