3. Find all extrema of the function $y=x \lg 2 x$.

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Solution: $y=x \lg 2 x, x>0, \quad y'=\lg 2 x+\frac{x \cdot 2}{2 x \ln 10}=\frac{\ln 2 x}{\ln 10}+\frac{1}{\ln 10}=0$, Answer: $x=\frac{e^{-1}}{2}, y=\frac{-1}{2 e \ln 10}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-04.jpg?height=245&width=371&top_left_y=1077&top_left_x=1571)