The mass of the part of a metal rod that lies between its left end and a point x meters to the right is $S=4 x^{2}$ . Find the linear density when x is 3 m.
A) 4
B) 20
C) 24
D) 12
E) 18

Question

Quizplus · Accepted Answer

The linear density is the derivative of the mass function with respect to x. The derivative of $S=4x^2$ is $S'=8x$. At $x=3$, the linear density is $8 \times 3 = 24$.

The Mass of the Part of a Metal Rod That S=4x2S=4 x^{2}S=4x2

The Mass of the Part of a Metal Rod That $S=4 x^{2}$