Question 976976
{{{f(x) = x^4 -x^3 - 20x^2 }}}

set {{{f(x) =0}}}

{{{0= x^4 -x^3 - 20x^2 }}}....factor out {{{x^2}}}

{{{0= (x^2 - x - 20)x^2 }}}....factor completely {{{(x^2 - x - 20) }}}, replace {{{-x}}} with {{{4x-5x}}}

{{{0= (x^2 - 4x+5x - 20)x^2 }}}......group

{{{0= ((x^2 - 4x)+(5x - 20))x^2 }}}

{{{0= (x(x - 4)+5(x - 4))x^2 }}}

{{{0= (x+4)(x-5)x^2 }}}

so, zeros are:

{{{0= (x+4) }}}=>{{{x=-4}}}-the multiplicity {{{1}}}
{{{0= (x-5) }}}=>{{{x=5}}}-the multiplicity {{{1}}}
{{{0= x^2 }}}=>{{{x=0}}}, -the multiplicity {{{2}}}


{{{ graph( 600, 600, -20, 20, -150, 90,  (x+4)(x-5)x^2) }}}

as you can see, there are {{{3}}} turning points of the graph of the function