Question 988985
{{{x}}}= the first number, so
{{{1/x}}}= the second number = the reciprocal of the first number, and
{{{S=x+1/x}}}= the sum.
The derivative is
{{{dS/dx=1-1/x^2=(x^2-1)/x^2=(x+1)(x-1)/x^2}}}
{{{dS/dx}}} is positive for {{{x<-1}}}, meaning that {{{S}}} is increasing in {{{"("}}}{{{-infinity}}}{{{","}}}{{{-1}}}{{{")"}}} .
{{{dS/dx}}} is negative for {{{-1<x<1}}}, meaning that {{{S}}} is decreasing in {{{"("}}}{{{-1}}}{{{","}}}{{{1}}}{{{")"}}} .
{{{dS/dx=0}}} for {{{x=-1}}}, where {{{S}}} has a maximum.
{{{dS/dx}}} is positive for {{{x>1}}}, meaning that {{{S}}} is increasing in {{{"("}}}{{{1}}}{{{","}}}{{{infinity}}}{{{")"}}} .
{{{dS/dx=0}}} for {{{highlight(x=1)}}}, where {{{S}}} has a minimum.