3. Find all extrema of the function $y=\frac{x}{8}+\frac{2}{x}$ on the interval $(-5 ; 10)$.
Solution: $y=\frac{x}{8}+\frac{2}{x},(-5 ; 10)$, Domain of Definition $x \neq 0$,

$y^{\prime}=\frac{1}{8}-\frac{2}{x^{2}}=\frac{x^{2}-16}{8 x^{2}}=\frac{(x-4)(x+4)}{8 x^{2}}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-16.jpg?height=178&width=732&top_left_y=1056&top_left_x=1230)

Answer: $y_{\max }(-4)=-1, y_{\min }(4)=1$.