On what interval(s) is the function f(x)=5/x+58 increasing?

Jul 29, 2017

$f$ is not $\uparrow$ in any interval contained in $\mathbb{R} - \left\{0\right\} .$

Explanation:

Recall that, a function (fun.)

$f \text{ is increasing } \left(\uparrow\right) , \mathmr{if} f ' \left(x\right) > 0.$

For given fun. $f , \text{ we have, } f ' \left(x\right) = - \frac{5}{x} ^ 2 < 0 , \forall x \in \mathbb{R} - \left\{0\right\} .$

Hence, it is not $\uparrow$ in any interval contained in $\mathbb{R} - \left\{0\right\} .$