# Find an equation of the tangent line to y=x+ 2/x at the point (2,3)?

May 23, 2018

$y = \frac{1}{2} x + 2$

#### Explanation:

$f \left(x\right) = x + \frac{2}{x}$ , ${D}_{f} = \mathbb{R}$*$= \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

For $x \ne 0$ we have

$f ' \left(x\right) = \left(x + \frac{2}{x}\right) ' = 1 - \frac{2}{x} ^ 2$

The equation of the tangent line at $M \left(2 , f \left(2\right)\right)$ will be

$y - f \left(2\right) = f ' \left(2\right) \left(x - 2\right)$ $\iff$

$y - 3 = \left(1 - \frac{2}{4}\right) \left(x - 2\right)$<=>#

$y - 3 = \frac{1}{2} \left(x - 2\right)$ $\iff$

$y = \frac{1}{2} x + 2$