Question 1155972


{{{f(x)=x^4/4 +x^3 +x^2}}}

find first derivative:

{{{f}}}′{{{(x)=4x^3/4 +3x^2 +2x}}}
{{{f}}}′{{{(x)=x^3 +3x^2 +2x}}}
{{{f}}}′{{{(x)=x(x^2 +3x+2)}}}

If {{{f}}}′{{{(x) > 0}}}, then {{{f}}} is {{{increasing}}} on the interval:


{{{x(x^2 +3x+2)> 0}}}

{{{x> 0}}}

or
{{{x^2 +3x+2> 0}}}

{{{(x + 1) (x + 2)>0}}}

{{{x>-1}}} or {{{x>-2}}}

 
{{{f}}} is {{{increasing}}} on the intervals: 

({{{-2}}},{{{-1}}}) U ({{{0}}},{{{infinity}}})


and {{{f}}} is decreasing on the interval:

({{{-infinity}}},{{{-2}}}) U ({{{-1}}},{{{0}}})



{{{ graph( 600, 600, -5, 5, -5, 5, x^4/4 +x^3 +x^2) }}}