Answer
(a) $ρ(1)$ = $6$ $kg/m$
(b) $ρ(2)$ = $12$ $kg/m$
(c) $ρ(3)$ = $18$ $kg/m$
Since $ρ$ is an increasing function, the density will be the highest at the right end of the rod and lowest at the left end
Work Step by Step
The mass is $f(x)$ = $3x^{2}$
so the linear density at $x$ is $ρ(x)$ = $f'(x)$ = $6x$
(a) $ρ(1)$ = $6(1)$ = $6$ $kg/m$
(b) $ρ(2)$ = $6(2)$ = $12$ $kg/m$
(c) $ρ(3)$ = $6(3)$ = $18$ $kg/m$
Since $ρ$ is an increasing function, the density will be the highest at the right end of the rod and lowest at the left end
