Question 1075016
Integrating,
{{{f(x)=x^3/3-2x-1/x+C}}}
So when {{{x=3}}},
{{{0=(3)^3/3-2(3)-1/3+C}}}
{{{0=9-6-1/3+C}}}
{{{0=9/3-1/3+C}}}
{{{C=-8/3}}}
{{{highlight(f(x)=x^3/3-2x-1/x-8/3)}}}
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Since the derivative is always positive in {{{x>0}}}, the function is increasing.
*[illustration r33.JPG].