1. ## linear density

The mass of a part of a metal rod that lies between its left and a point x meters to the right is 3x^2 kg. Find the linear density when x is:

(a) 1 m

(b) 2 m

(c) 3 m

Also, where is the density the highest? The lowest?

If anyone could help me out with this one that would be great! maybe show me how to do a,b or c and then I can try the rest? thanks!

2. Originally Posted by thecount
The mass of a part of a metal rod that lies between its left and a point x meters to the right is 3x^2 kg. Find the linear density when x is:

(a) 1 m

(b) 2 m

(c) 3 m

Also, where is the density the highest? The lowest?

If anyone could help me out with this one that would be great! maybe show me how to do a,b or c and then I can try the rest? thanks!
Let the mass to the right of a point $x$ be $F(x)$

The linear density at $x$ is the limit of the mass in a small element of the rod near $x$ divided by the length of the element, so:

$f(x)=\lim_{\delta \to 0} \frac{F(x+\delta/2)-F(x-\delta/2)}{\delta}=F'(x)$

In this case $F(x)=3x^2$

RonL