Let's factorise the expression

#3x^2-11x-4=(3x+1)(x-4)#

Let #f(x)=3x^2-11x-4#

Now, we can make the sign chart

#color(white)(aaaa)##x##color(white)(aaaaa)##-oo##color(white)(aaaa)##-1/3##color(white)(aaaaa)##4##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##3x+1##color(white)(aaaaa)##-##color(white)(aaaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-4##color(white)(aaaaaa)##-##color(white)(aaaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaaaa)##-##color(white)(aaaa)##+#

Therefore,

#f(x)<=0# when #x in [-1/3,4]#