Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The function $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 }$ describes the volume of a cube, $\mathrm { f } ( \mathrm { x } )$ , in cubic inches, whose length, width, and height each measure $x$ inches. Find the instantaneous rate of change of the volume with respect to $x$ when $x = 4$ inches.

A) 12 cubic inches per inch
B) $49.21$ cubic inches per inch
C) 48 cubic inches per inch
D) 192 cubic inches per inch