Solve the problem.
-The function f $$f ( x ) = x ^ { 3 }$$ describes the volume of a cube, f(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

Question

Quizplus · Accepted Answer

The instantaneous rate of change of the volume with respect to x is found by taking the derivative of the volume function $f(x) = x^3$ with respect to x, which gives $f'(x) = 3x^2$. Substituting $x = 4$ inches into $f'(x)$ gives $f'(4) = 3(4)^2 = 3(16) = 48$ cubic inches per inch.

Solve the Problem f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3

Solve the Problem $f ( x ) = x ^ { 3 }$