![image](https://tex.z-dn.net/?f=y%3Dx%5E2%5Ccdot+e%5E%7Bx%7D%5C%5C%5C%5Cy%27%3D2x%5Ccdot+e%5E%7Bx%7D%2Bx%5E2%5Ccdot+e%5E%7Bx%7D%3De%5E%7Bx%7D%282x%2Bx%5E2%29%3D0%2C%5C%5C%5C%5Ce%5E%7Bx%7D%3E0%5C%3B+pri%5C%3B+x%5Cin+R%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+2x%2Bx%5E2%3D0%5C%5C%5C%5Cx%282%2Bx%29%3D0%5C%5C%5C%5Cx_1%3D0%2C%5C%3B+x_2%3D-2%5C%5C%5C%5C%2B+%2B+%2B+%2B%28-2%29+-+-+-+-%280%29%2B+%2B+%2B+%2B+%2B%5C%5C%5C%5Cx_%7Bmin%7D%3D0%2C%5C%3B+y_%7Bmin%7D%3D0%5C%5C%5C%5Cx_%7Bmax%7D%3D-2%2C%5C%3B+y_%7Bmax%7D%3D%28-2%29%5E2%5Ccdot+e%5E%7B-2%7D%3D4e%5E%7B-2%7D%3D%5Cfrac%7B4%7D%7Be%5E2%7D)
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">