Answer
$f'(x)=12x-5$;
$ f'(-2) = -29$;
$ f'(0)=-5$;
$f'(3)=31$;
Work Step by Step
$f(x+h)=6(x+h)^{2}-5(x+h)-1=6x^{2} + 12xh +6h^{2} -5x - 5h -1$
$f(x+h) - f(x) =6x^{2} + 12xh +6h^{2} -5x - 5h -1 -6x^{2}+5x +1=12xh+6h^{2}-5h$
$\frac{f(x+h) - f(x)}{h}=12x+6h-5$
$f'(x) = \lim\limits_{h \to 0} (12x+6h-5) =12x+6(0)-5=12x-5$
$ f'(-2) = -29$
$ f'(0)=-5$
$f'(3)=31$
