Question 1155431

{{{f(x)= x^2* ln (x^2+3)}}}-> parabola, opens up

domain:

({{{-infinity}}},{{{infinity}}})

range:

{ {{{f}}} element {{{R}}} : {{{f>=0}}}} (all non-negative real numbers)

x-intercept:

{{{0= x^2*ln(x^2+3)}}}

{{{x=0}}}

=>x-intercept at origin

 
y-intercept:

{{{y= 0^2*ln(0^2+3)}}}

{{{y=0}}}

=>y-intercept at origin


=> minimum is at origin

so, the interval on which {{{f}}} is increasing is 

({{{0}}},{{{infinity}}})


 and the interval on which it is decreasing is

({{{-infinity}}},{{{0}}})


{{{ graph( 600, 600, -10, 10, -10, 10, x^2* ln (x^2+3)) }}}