Question 469317
{{{F(x) = (x (9 x^2-4))/((x-3) (x-1)^2)}}}

{{{F(x) = (x(3 x-2) (3x+2))/((x-3) (x-1)^2)}}}

{{{F(x) = (9 x^3)/((x-3) (x^2-2 x+1))-(4 x)/((x-3) (x^2-2 x+1))}}}


{{{ graph( 500, 500, -40, 50, -95, 50, (x*(3x-2)(3x+2))/((x-3)*(x-1)^2)) }}}


local maxima:

at {{{x=0.5}}} max-{{{F(x) = (9x^3-4x)/((x-3)(x^2-2 x+1))=-0.875/(-2.5*0.25)=-0.875/(-0.625)=1.4}}}

at {{{x=1.7}}} max-{{{F(x) = (9x^3-4x)/((x-3)(x^2-2 x+1))=37.417/(-1.3*0.49)=37.417/(-0.637)=58.7}}} 


local minimum:


at {{{x=-0.3}}} min-{{{F(x) = (9x^3-4x)/((x-3)(x^2-2x+1))=0.957/(-3.3*1.69)=0.957/-5.577=-0.17}}}