0\; pri\; x\in R\; \; \to \; \; 2x+x^2=0\\\\x(2+x)=0\\\\x_1=0,\; x_2=-2\\\\+ + + +(-2) - - - -(0)+ + + + +\\\\x_{min}=0,\; y_{min}=0\\\\x_{max}=-2,\; y_{max}=(-2)^2\cdot e^{-2}=4e^{-2}=\frac{4}{e^2}" alt="y=x^2\cdot e^{x}\\\\y'=2x\cdot e^{x}+x^2\cdot e^{x}=e^{x}(2x+x^2)=0,\\\\e^{x}>0\; pri\; x\in R\; \; \to \; \; 2x+x^2=0\\\\x(2+x)=0\\\\x_1=0,\; x_2=-2\\\\+ + + +(-2) - - - -(0)+ + + + +\\\\x_{min}=0,\; y_{min}=0\\\\x_{max}=-2,\; y_{max}=(-2)^2\cdot e^{-2}=4e^{-2}=\frac{4}{e^2}" align="absmiddle" class="latex-formula">