The function [f( x ) = x 2 + 2 x] has a local minimum at

Question

The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at

Accepted Answer

$$f\left( x \right) = {x \over 2} + {2 \over x} \Rightarrow f'\left( x \right) = {1 \over 2} - {2 \over {{x^2}}} = 0$$

$$ \Rightarrow {x^2} = 4$$ or $x=2,-2;$ $$\,\,\,\,\,f''\left( x \right) = {4 \over {{x^3}}}$$

$$f''{\left. {\left( x \right)} \right]_{x = 2}} =  + ve \Rightarrow f\left( x \right)$$

has local min at $x=2.$

Solutions · 1